My Dear Sir: 

Observe there is nothing' contained in 
this Pocket Edition but practical solid 
matter upon the subject it treats; had it 
been printed with larger type and wider 
margin (generally used to make a larger 
book), it would have made a volume 
four times the size, and too cumbersome 
for the pocket. Our object has been to 
condense into the smallest practicable 
space, and believe the surveyor will ap- 
preciate the motive. 

Very respectfully, 

THE PUBLISHERS. 



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A PRACTICAL TREATISE 



ON 



LAND SURVEYING 



OR THE 



SURVEYOR'S GUIDE, 



CONTAINING 

Practical Rules for Locating Lost Corners and Running 
Lines; How to Obtain the Variation of the Needle 
and its Application, and Much Other Infor- 
mation of Practical Value to the 
Surveyor and the Public. 




EDWARD SARGENT, C. E. / 

/ / 



1895. 



*' To develop in each individual all the perfection of which 
he is susceptible is the object of education." — Kant. 






Copyright, March 18, 1895, 

BY 

EDWARD SARGENT, 
W. H. H. CASH. 



PRKSS OF 

THE EVENING WISCONSIN CO. 

MILWAUKEE. 



&-ast 



IN ID EX- 



CHAPTER I. 

Plane Trigonometry I 

Instructions to Surveyors ". 2 

Diagram of Back and Fore Sights 2 

Local Attraction 3 

Surveyors' Outfit 3 

Adj us ting the Chain 4 

Advantages of a Steel Tape 4 

Adjustment of the Compass 4 

Adjustment of the Transit 5 

Diagram of Magnetic Variation 7 

Variation of the Needle 8 

Diagram of Elongations of the North Star 9 

Establishment of a Meridian Line 9 

Due E. and W. Line 12 

Rule for Retracing Section Lines , 12 

Rule for Retracing Lines Described by Metes and Bounds 12 

To Reduce Magnetic Bearings to True 13 

To Reduce True Bearings to Magnetic 13 

To Find the Angles Between Two Lines by Bearings 

From the Same Corner 13 

CHAPTER 11. 

Subdividing and Describing Land 15 

Diagram of Township " Seven Ranges " 16 

Diagram of Township " N. W. Territory " 16 

CHAPTER III. 

Geographical Position of Meridian and Base Lines 19 

First Principal Meridian 19 

Second Principal Meridian 19 

Third Principal Meridian 19 

Fourth Principal Meridian 19 

Fifth Principal Meridian 20 

Sixth Principal Meridian 20 

Michigan Meridian 20 

Tallahassee Meridian 20 

Saint Stephens Meridian 20 

Huntsville Meridian 20 

Choctaw Meridian 20 

Washington Meridian 21 

Saint Helena Meridian 21 

Louisiana Meridian 21 

New Mexico Meridian 21 

Great Salt Lake Meridian 21 



iv. THE SURVEYOR'S GUIDE 

Boise Meridian 21 

Mount Diablo Meridian 21 

San Bernardino Meridian 21 

Humb olt Meridian 22 

Willamette Meridian 22 

Montana Meridian 22 

Gila and Salt Lake Meridian 22 

Indian Meridian 22 

Convergency of Range Lines 22 

How to Obtain Longitude 23 

How to Obtain Latitude 23 

Table of Convergency of Meridians 24 

CHAPTER IV. 

Survey of N. W. Territory 25 

Method of Subdividing Townships 26 

Remarks on Lost Corners 27 

Remarks on Lost Corners by the General Land Office 27 

General Land Office Do Not Comprehend Proportionate 

Measurements 28 

CHAPTER V. 

Errors in Government Surveys 29 

What Should Have Been 29 

Diagram of a Township 30 

A Township Very Uneven and Brushy 30 

Diagram of Town 22 N., R.4E 32 

A Surveyor Not Always Within Prescribed Limit 33 

Sections are Independent Rectangular Tracts 35 

CHAPTER VI. 

Required Locus of Lost Corners 36 

Diagram of Lost Corners 36 

Diagram of Lost Corners 37 

Diagram of Lost Corners 38 

Re-establishment of Lost Corners 38 

Lost Interior Quarter Section Corners 38 

Lost Quarter Corner Closing upon the North and West 

Boundaries of the Township 39 

Lost Quarter Section Corner on Township Boundaries 39 

Lost Interior Section Corner 39 

Closing Section Corners 41 

Section Corner Common to Two Townships 42 

Section Corner Common to Four Townships 43 

Lost Corner Where Corners Are Lost on All Sides 44 

Lost Meander Corners 45 

Retracing of Meander Lines 45 

Locating a Corner by Witness Trees 47 

Remarks on Lost Corners 48 

On Chaining 49 



THE S UR VE Y01? S G UIDE v . 

Preliminary Work Locating a Lost Corner 51 

Criminal Destruction of Corners 51 

Section Subdivided 52 

State Engineers 52 

Expense of Survey 53 

CHAPTER VII. 

Subdividing Sections into Quarter Sections 54 

Into Sixteenths 54 

Fractional Sections 54 

Correcting Departure 54 

Examples of Correcting Departure 55 

Diagram of Departure 56 

CHAPTER VIII. 

Missing Corners 57 

Ability of a Surveyor to Trace Lost Corners 57 

Witness Trees 57 

Testimony of Living Witnesses 57 

Searching for a Corner 57 

Evidence of Living Witnesses Unreliable 58 

Line Trees .- 58 

Geographical Descriptions in Field Notes 58 

Better Abide by the Decision of an Expert Surveyor 58 

Often no Justice in Jury Trials 59 

A One-quarter Post out of Line 59 

Corners in a Prairie County, How Designated, Definition 

of Surveyor's Works 60-62 

CHAPTER IX, 

Surveying and Subdividing Lands by Metes and Bounds... 63 

Lands Surveyed by Metes and Bounds 63 

Original Surveys Over Two Centuries Old 63 

Variation of Needle Not Constant 63 

Rule for a Survey Described by Metes and Bounds 63 

Boundary Lines Permanently established 64 

Permanent Starting Point Necessary 64 

Latitude and Departure 65 

Table of Corrected Latitude and Departure . 67 

Surveys by Triangulation 67 

CHAPTER X. 

Contents of Land 69 

Square Acre to Lay Out 69 

Rectangle to Lay Out 69 

Trapezoid ; 69 

Trapezium 70 

Right Angle Triangle 70 

Tract Bounded on One Side by a Stream 70 

Circle, Area of. 71 

To Lay Out a Given Area in a Square 71 



vi. THE SURVEYOR'S GUIDE 

To Lay Out a Given Area, the Adjacent Sides to have a 

Given Ratio 71 

To Divide a Trapezoid into Two Parts of Given Ratio 72 

Computation by Latitude and Departure 72 

Table of Computation by Latitude and Departure 74 

Metes and Bounds Often the Most Reliable 75 

CHAPTER XI, 

Simple Method of Measuring the Distance Across a 

Stream 76 

Obstacles in Line 77 

Measuring Angles 77 

Leveling 78 

Tables 79 

Time of Eastern and Western Elongation of North 

Star 80 

Azimuth of North Star 81 

Chains and Links Reduced to Feet 82 

Departure for i / to 6o / at 10 to 80 Chains 83-84 

Diagram of Territory Subdivided into Townships 85 

Legal Evidence and Opinions 86 



THE SURVEYOR'S GUIDE vii. 

EXPLANATIONS OF SYMBOLS. 

— Equal to, as 12 inches — I foot, 8x8 = 64. 

_|_ Plus or more signifies addition, as 4+6 = 10. 

— Minus or less signifies subtraction, as 15—5 = 10. 
X Multiplied by, as 15X5 = 75> 

-1- Divided by, signifies division 72-^9 = 8. 

: Is to :: so is : to, signifies proportion as 2:4 :: 8: 16. 

. •. Signifies hence or therefore. 

\ • Because. 

-/ Signifies square root of the number. 

<yj Difference, signifies when placed between two quanti- 
ties that their difference is to be taken, it being unknown 
which is greater. 

10 Superior signifies square of a number, as ioxio = 100. 

One hundred words — one folio. 

of// /// Signify degrees, minutes, seconds, thirds. 

2' 2 /r Denotes dimensions in feet or inches. 

Numerals were derived directly from the Arabs. They 
were introduced into Europe about the year 960, by Gebart, 
who was Pope Sylvester II. 

Logarithms were invented by Napier of Scotland, who 
died in 161 7. 

Notation by exponents was introduced by Descartes, who 
died in 1650. 

Newton and Leibnitz discovered the method of fluxions in 
the years 1684-6. 

Pythagorus, in the year 590 B. C, discovered the funda- 
mental properties, that the square of the hypothenuse is equal 
to the sum of the squares of the two sides. 

Euclid appeared in the year 300 B. C. 

The Greeks and all other ancient nations used letters and 
other characters for arithmetical operations, but of arithmetic 
knew very little. 



VIII. THE SURVEYOR'S GUIDE 

PREFACE. 

During a professional experience of more than thirty years 
on railroad and government construction I have had more or 
less to do with "government public land surveys." Cer- 
tainly, sufficient to learn that the survey of public lands has 
been very imperfectly performed, and very little understood 
by the public; that to retrace an original line and restore a lost 
corner to its original locus is impossible; that books on sur- 
veying contain no practical general information on the sub- 
ject; that the surveyor in the performance of his work gropes 
his way in darkness searching for that which is lost. 

A work of general information upon the subject of public 
land surveys is a desideratum long felt by surveyors and attor- 
neys-at-law. To supply this want the author has endeavored 
to compile a work which may enlighten the public and 
remove much doubt from the mind of a surveyor. 

In his labor of compilation he has been materially aided 
by a "Manual of Surveying Instructions, for the Survey oi 
the Public Lands," and a pamphlet on Restoration of Lost 
and Obliterated Corners, published by the Commissioners of 
the General Land Office of the United States. 

The author hopes a surveyor may find herein instruction 
which will more surely guide him toward the original locus of 
a lost corner. 

The author believes, that in a general review of public 
land surveys, much information is given to the public un- 
known to them. Certainly unknown to himself until neces- 
sary investigation revealed to him the careless work of a 
United States deputy surveyor. Practically, it is discovered 
that surveys widely differ from instructions and field notes ; 
hence, the surveyor necessarily must depend mostly upon 
theory in the performance of his work. 

Speculating upon existing conditions the rules herein 
given, f< though not absolute," are in harmony with original 
intent and must obtain more satisfactory result than propor- 
tionate measurements. 

EDWARD SARGENT, 

Grand Rapids, Wis. 



CHAPTER I. 

PLANE TRIGONOMETRY. 

In every plane triangle there is six parts — three sides and 
three angles. 

When three parts are known all the other parts can be 
found by computation. 

The complement of an angle is the difference between it 
and 90 

The supplement of an angle is the difference between it 
and 180 . 

Examples: 90 — io° = 8o° — the complement. 
180 — io° — 170 — the supplement. 

Triangle is a figure of three sides. 

Equilateral triangle has all sides equal. 

Isoscles triangle has two sides equal. 

Scalene triangle has all sides unequal. 

Right angled triangle has one right angle = 90 . 

Oblique angled triangle has no right angle. 

Acute angled triangle has all angles acute. 

Obtuse angled triangle has one obtuse angle. 

Pentagon, a figure with five sides. 

Hexagon, a figure with six sides. 

Heptagon, a figure with seven sides. 

Octagon, a figure with eight sides. 

Nonagon, a figure with nine sides. 

Decagon, a figure with ten sides. 

Undecagon, a figure with eleven sides. 

Dodicagon, a figure with twelve sides. 

Quadrant, is one-fourth part of a circle. 

Semi-circle, is one-half of a circle. 

Radius, is a line drawn from the center of a circle to the 
circumference. 

Arc, is any part of the circumference of a circle. 

1 



2 THE SURVEYOR'S GUIDE 

Angle, a point where two lines meet; a difference of direc- 
tion of two lines, and is either right, acute, or obtuse. 

Right angle is made by a line perpendicular to another 
falling upon it. 

Acute angle is less than a right angle. 

Obtuse angle is greater than a right angle. 

INSTRUCTIONS TO SURVEYORS. 

Note. — Surveying first introduced A. D. 219. 

The surveyor should ever have in mind the adage, "What- 
soever is worth doing at all is worth doing well." Now, he 
cannot do well without good instruments and outfit. With a 
common pocket compass he is able to trace a line in timber, 
but cannot run a straight line from corner to corner; it 
requires more skill than casual work can accomplish. Sur- 
veyors often boast of intersecting a corner with a pocket com-' 
pass, but it is no evidence the work has been done correctly. 
It is very seldom that a line run with a transit instrument 
intersects the corner. 

Bear in mind no dependence can be placed in the needle 
readings ; always run by back and fore sights equidistant 
from the instrument, the average of the readings (except there 
be energetic local attraction) will approximate the true course. 

The importance of running by back and fore sights becomes 
apparent in observing the effect of "Diurnal Variation." 
The variation of the needle increases from morn until 
the sun is at meridian height, when it decreases until at 
night it is the same original reading of the morning; hence 
at noon the needle reads from 6 / to I5 / more than at morn or 
eve. The departure for 15' measures 23 feet to the mile. 

It is plain that a line run with magnetic bearings traces a 
curved line. 

DIAGRAM OF BACK AND FORE SIGHTS. 



I 



i» R 



_X_ ^-JS. 



B Records tke. £««>-»«£. 



The surveyor sets his instrument at A, records the bearing, 
and sets front flag at B; he then moves to B, and the back flag- 



THE SURVEYOR'S GUIDE 3 

man sets his flag at A; he takes a sight on A and in the op- 
posite direction, in line, sets his front flag at C. At A his reading 
was N. 6° W., at B, sighting back to A, it is N. 6° ig' 
W., indicating slight local attraction. Having set front flag at 
C he moves to C and the back flag to B; he takes a sight on 
B and sets at 20 rods in the opposite direction his front flag, 
recording the bearing; he thus proceeds to the desired point 
of intersection, at which point he may be at the right or left 
of the corner. If there be no energetic local attraction, the 
average of his needle readings will be the bearings of the line 
run, which is, say, N. 6° 5 / W., he measures at right angles to 
the line run, the distance to the post and computes the angle 
by one of the rules found on page 55. If at the right of 
the post the bearing will be N. 6° 5' W. + the angle found, if 
to the left the bearing will be N. 6° 5' W. — the angle found. 

LOCAL ATTRACTION. 

Mineral deposits or some other unknown cause, called 
"Local Attraction,' 1 ' 1 often deflect the needle from a course. 
Back and fore sights detect local attraction. 

Obtain all the information possible; accept as much as will 
aid you in the work, then rely upon your own judgment and 
go ahead; never be in a hurry; take proper time to do your 
work well; the effect of rushing is too plainly stamped upon 
the work of government surveyors. 

SURVEYOR'S OUTFIT. 

Two flag poles, steel pointed, 8 feet long, and divided 
into foot spaces, each painted alternately red and white. 
The surveyor will find their use more satisfactory than rough 
poles cut in the field. 

One 66 feet (4 rods) steel chain with links and rings 
brazed; steel chains with links and rings brazed are much 
the strongest and lightest, and do not elongate as quickly as 
one of iron not brazed. (Note. — Steel tapes are now gener- 
ally used and preferred by engineers and surveyors.) 



4 THE SURVEYOR'S GUIDE 

Eleven steel arrows or marking pins. (Not?:. — By making 
them of steel, much smaller wire can be used than of iron, the 
utility of a small pin will be demonstrated in proper place 
further on; bright red tags should be fastened to the pins.) 

One 5^ inch vernier compass with Jacob staff mountings. 

One surveyor's transit with light tripod mountings. 
Note. —The use of the transit quickly commends advan- 
tages not found in the compass. 

Two straps or belts, to which is attached an open ring; 
they are buckled around the body of the chainman, for con- 
veniently carrying marking pins, they avoid the loss of a pin; 
consequently prevent vexation and delay. A narrow strap or 
belt buckled around the waist on which leather tally buttons 
are easily slipped from one side to the other for marking 
tallies. (Note. — Compasses and surveyor's transit are now 
made with a dial index for registering tallies.) 

ADJUSTING THE CHAIN. 

It is the utmost importance that a surveyor has a stand- 
ard measure, marked 66 feet long on a floor, and at any time 
test his chain or tape. 

Note. — A four-rod chain contains ioo links, and gener- 
ally twice that number of rings, making 300 parts liable to 
abrasion. Suppose you find your chain one inch too long, 
the wear on each connection is only g-J D part of an inch; 
hence you can readily appreciate the advantage of using a 
steel tape. 

Note. — Standard measure is a brass scale 82 inches in 
length. A yard is measured between the 27th and 63d inches 
of it, which at a temperature of 62 is standard yard. 
"ADJUSTING THE COMPASS." 

Note. — Mariner's compass discovered in China, A. D. 1 120. 

The Levels. — First bring the bubbles into the center, 
then turn the compass half-way around. If the bubbles run 
to either end of the tube, loosen the screws under one end, 
and tighten them under the other, repeat the operation until 
the bubbles remain in the center during a complete revolution 
of the compass. 



THE SURVEYOR'S GUIDE 5 

To ascertain whether the sights are plumb, suspend a fine 
cord made vertical by a plumb bob or weight in water. 
Should the slit be out of plumb adjust the sight by filing the 
under side until the slits and cord coincide. 

TO ASCERTAIN WHETHER SIGHTS AND CENTER ARE 

IN LINE. 

About three or four hundred feet from the compass set 
one of your flagstaffs, in the opposite direction, distant three 
or four hundred feet, set the other staff; revolve your compass 
one-half around, and if in a straight line, your sights will 
bisect both staffs. If they do not, the compass is defective ; 
send it at once to the manufacturer for repairs. 

The Needle. — Set your needle at o or N. Observe 
whether the needle cuts opposite degree or S. If it does 
not, bend the center pin until it does. Turn the compass half- 
way around. Note whether it now cuts opposite degrees N. 
and S., if not, correct half the error by bending the needle, and 
the other half by bending the pin; repeat the operation until 
perfect reversion is obtained in these positions. The needle 
is now in a straight line; if in any other position an error is 
manifested; bend the center pin until the needle will reverse 
on any point. 

ADJUSTMENT OF THE TRANSIT. 

The principal adjustments of the transit are: 
(i) The levels. 

(2 ) The line of collimation. 

(3) The standards. 

Note. — For the convenience of the surveyor the following 
abbreviated adjustments are taken from a manual of instru- 
ments, published by W. & L. E. Gurley, Troy, N. Y., and 
sent with every instrument purchased of the firm. 

To Adjust the Levels. — Set up the instrument upon its 
tripod as nearly level as may be, and having undamped the 
plates, bring the two levels above on a line with the two pairs 
of leveling screws; bring the bubbles to the center with the 
leveling screws; turn the instrument half-way around. If 



6 THE SURVEYOR'S GUIDE 

the bubbles remain in the center they need no correction; if 
they do not, adjust half the error by turning with your adjust- 
ing pin the screws at the ends of the levels and the other hall 
by the leveling screws. Repeat the operation until the bub- 
bles remain in the center during a complete revolution of the 
instrument. 

TO ADJUST THE LTNE OF COLLIMATION. 

Note.- — The word collimation simply means a straight 
line intersecting the wires in the optical axis of the telescope. 

Set the instrument firmly on the ground and level it care- 
fully; bring the wires distinctly into the focus of the eye- 
piece. Take a sight on some well-defined point or a plumb- 
line made vertical by suspending the bob in water. Observe 
if the vertical wire is plumb with the plumb-line. Should 
any deviation be manifested, loosen the cross wire screws 
and move the ring around until the error is corrected. 
Clamp the instrument firmly and at about four or five hun- 
dred feet set your flagstaff, revolve the telescope and set your 
flag about the same distance in the opposite direction, taking 
special care that the position of the instrument is not in the 
slightest degree disturbed. Unclamp the instrument and 
turn it half-way around. Sight to your first flagstaff, clamp 
the instrument and revolve the telescope. If it bisects the 
opposite flag the wires are in adjustment and in the same 
straight line. If the wires are at one side of the last flag, set 
flag one-half the distance between. Adjust the vertical wire 
by loosening one of the screws and tightening on the opposite 
side. (Remember the eye-piece inverts the position of the 
wires and the operator must proceed as if to increase the 
error.) Again sight to the first flag, revolve the telescope 
and observe if it bisects the other flag. Repeat the opera- 
tion until both flags are bisected, proving the wires are in 

adjustment. 

TO ADJUST THE STANDARDS. 

In order that the wires may trace a vertical line it is neces- 
sary that both standards should be of precisely the same 
height. Level the instrument; fix the wires on the top of 



THE SURVEYOR'S GUIDE 



a lofty spire; then bring the telescope down until the wires 
bisect a point at the base; turn the instrument half around; 
fix the wires on the lower point and raise the telescope to top 
of the spire; if the wires bisect it, the vertical adjustment is 
effected. If they are thrown toeither side, the standard oppo- 
site that side is the highest, the apparent error being double 
that due to this cause. Raise or lower the bearing of one end 
of the axis until adjustment is made and the wires bisect in 
reverse position both points. 

DIAGRAM OF MAGNETIC LINES "VARIATION OF 

COMPASS." 

Note. — Magnetic lines are drawn right lines, but they 
bend east or west of a right line, forming irregular curves. 
Straits of Mackinaw. 




* n* T/or^ 



West /an^T.o! 



8 THE SURVEYOR'S GUIDE 

"VARIATION OF THE NEEDLE." 

Note. — First observed in the mariner's compass, A. D. 
1500. 

Very few surveyors comprehend the term " Variation of 
the Needle." The lines of magnetic variation are not true 
north and south courses; they attract the needle as the dis- 
tance is east or west of a line of no variation now passing 
through the Strait of Mackinaw, Mich., Toledo, Ohio, and 
crossing the coast near Charleston, S. C; east of this line the 
needle is attracted west, and west of it the needle is attracted 
east, and these attractions increase as the needle is 'carried 
farther east or west of the line of no variation. West of this 
line the variation is now annually decreasing and east of it the 
variation is now annually increasing. 

Note. — The annual increase in latitude 44 30', longitude 
73 , is about 2^ minutes, and the annual decrease in the same 
latitude, longitude 90 30', is now about -^ s minutes; these 
quantities are closely approximate; the latter based upon 

OBSERVATION TAKEN IN THE YEAR 1888. 

This annual increase and decrease is not a constant quan- 
tity and is liable to change. In a Manual of Instructions for 
the Survey of the Public Lands, issued by the Commissioner 
of the General Land Office, he gives the annual change in 
Wisconsin 3.30 minutes, but an observation obtainetl in 1888, 
makes the annual change in longitude 90°30 / , latitude 44°3o / , 
2 T 8 ff 5 g minutes. 

Note. — The magnetic lines are not right lines, but are 
irregular curved lines, bending at different points east or 
west of a right line. 

The line of no variation has been moving west since A. D. 
1800. 

Variation of the needle in 1875 (U- S. Coast Survey) at 
Milwaukee was 5 48', at Chicago 5 , at St. Paul io° 30', and 
at Detroit o° 3'. 



THE SURVEYOR'S GUIDE 



9 



DIAGRAM SHOWING THE POSITION .OF THE NORTH 

STAR WHEN AT ITS ;EASTERN OR 

WESTERN ELONGATION. 



Western ETlot^aTi'ory 



Edaterfi ElentfaTior^. 




Note. — That you may have a check upon your work take 
observations on both eastern and western elongations. 

ESTABLISHMENT OF A MERIDIAN LINE. 

Every surveyor or, better, every county should establish suita- 
ble permanent monuments in a true north and. south line, that 
from off it a surveyor may at any time obtain the variation in 
the latitude and longitude where located. 

Note. — No surveyor can do correct work without knowing 
the annual variation. 

To establish a true north and south line, the following 
method is the most simple one for the surveyor: 

Drive two posts firmly in the ground, and in line east and 
west, about four feet apart; cut them off level about four 
feet above the ground, and spike across their tops a surfaced 
2 // x 6 // . To an inch board fix one of your compass sights 



10 THE SURVEYOR'S GUIDE 

and place it loosely on top of the 2 // x6 // ; about fifty feet north 
of the stand fix firmly in the ground a tall pole, so the top 
will be about two feet above a line of sight from the compass 
sight or transit and north star; from the top of the pole sus- 
pend a plumb-line, and to prevent vibration, suspend the bob 
or weight in a tub of water; near the plumb line fix a lantern 
or light in such a position, that from the compass sight or 
transit the plumb-line is distinctly brought in view. You 
are now prepared to take an observation. Select a still, moon- 
light night at a time of year when the eastern or western 
elongation occur between the hours of 8 o'clock and 12 o'clock 
p. M. The north star is distant from the pole 1° 17'; in 
revolving around the pole its apparent motion is east to west 
and west to east; when moving east or west at the time it 
has reached its eastern or western elongation (so-called) and 
before it commences to move west or east, it apparently 
remains a short time stationary. This is the time to take an 
observation, as follows: From the table of elongations obtain 
the time it reaches its eastern or western elongation; just 
before the time, bring the compass sight or transit, plumb- 
line and north star into line; move the compass sight or 
transit as the star moves east or west until it reaches its east- 
ern or western elongation, readily comprehended by its 
remaining stationary a short time before commencing to move 
west or east. Observe the compass sight or transit, plumb- 
ine and north star in line, fasten the compass sight and leave 
the work until morning; in the morning take the bearing of 
the eastern or western elongation; find in the azimuthtable the 
azimuth angle for the year and the latitude in which it is 
located, and if variation is east add it to the bearing of eastern 
elongation and subtract it from bearing of western elongation. 
If variation is west, subtract from the bearing of eastern 
elongation and add to the bearing of western elongation; the 
bearings so obtained is the variation. In this line fix perma- 
nent monuments about three hundred feet apart and obtain a 
permanent true north and south line for future observation. 



THE SURVEYOR'S GUIDE 11 

Note. — If a transit is used it will be a more satisfactory 
observation, but the points in line of eastern or western 
elongation should be established before leaving. With the 
transit in line revolve the telescope and at about two hundred 
or more feet south, fix a point in line from which to measure 
the azimuth angle in the morning. 

Magnetic azimuth is an arch of the horizon intercepted 
between the vertical circle passing through the center of a 
heavenly body and the magnetic meridian. 

EXAMPLE. 

Suppose the variation is east, and in latitude 44° 30', lon- 
gitude 90 30', an observation is taken on the north star 
when at its eastern elongation. The bearing of the eastern 
elongation is determined N. 3 io' W. The azimuth angle is 
i° 46'; 3 io'-f i° 46' = variation 4 56' E., the approximate 
variation in the year 1894, in latitude 44 3c/, longitude 90 
30 / ; if the observation had been taken when at its western 
elongation, the bearing of the western elongation would have 
been N. 6° 42 / W. 6° 42'— 1° 46' = 4 56' E., the same as 

before. 

APPLICATION. 

In the year 185 1 a township in latitude 44" 30', longitude 
90 30', was subdivided and the variation of one of the section 
lines noted io° E. 

West of the line of no variation, the variation is decreasing 
approximately 2j 8 ^ 5 5 minutes annually. The survey was made 
forty-three years ago: 2 i 8 5 gX43 = 2 ° 2 ' = the total decrease 
since 185 1, add it to the present variation, 4 56', and we 
obtain 6° 58'' for the variation in 1851; from the variation io° 
subtract the variation 6° 58' and we obtain the true bearing 
of the line N. 3 2 / W. 4 56 / +3° 2 / = 7 58' or io°— 2° 2 / 
= 7 58' to set vernier. Suppose, in latitude 44 30', longi- 
tude 73 , the bearing on the north star at its eastern elonga- 
tion is N. 15 44 / E. Subtract the azimuth angle, i° 46', and 
we obtain 14 W., the present variation. If the observation 
had been taken at western elongation, the reading would have 
been N. 12 14' E. + i° 46' = 14 W., as before. 



12 THE SURVEYOR'S GUIDE 

APPLICATION. 

In latitude 44 3c/, longitude 73 , in the year 1S51, forty- 
three years ago, a line was run on a magnetic bearing N. 4S 
W. The present variation is 14 W. It is evident the varia- 
tion in the year 185 [must be obtained. Suppose the annual 
increase has been 2 f 5 , minutes 2.5x43= i° 47', total increase; 
14 — 1° 47 7 = 12 13', the variation in 185 1; N. 48 W. + 12 
13' W. = N. 6o° I3 / W. , the true bearing of the line in 1851. 
Set your vernier at 14 W. and run N. 6o° 13' W. and you 
retrace the original line. 

In the year 1888 the question was asked, viz.: If a deed 
called for a due east and west line, how would you obtain it ? 

By taking at a known point in the line an observaton on 
the " north star," obtain the true meridian and at right angles 
run the line. An observation was taken and a variation 5 
15' E. obtained, at right angles run the line, which proved to 
be nearly parallel with the section line about 20 rods north. 

Note. — The term due E. and W. in a deed may be ques- 
tionable in intent. It is intended that all section lines are 
run true meridian, hence the term due E. and W. may apply 
the rule controlling the subdivision of a section, but it would 
bean issue of fact for the court to decide and not the surveyor. 

RULE FOR RETRACING SECTION LINES. 

If variation is east, multiply the annual decrease by 
the number of years since survey was made and subtract the 
product from Government variations, the remainder is the 
degrees or minutes to set vernier. If variation is west, multi- 
ply the annual increase by the number of years since survey 
was made, add the product to government variaiton and the 
sum is the degrees and minutes to set vernier. 

Rule for Retracing Metes and Bounds. — For true bearings 
set the vernier at present variation, and run the bearings 
noted. 

For Magnetic Bearings. — 'Multiply the annual increase or 
decrease by the number of years since survey was made. Add 
or subtract it from present variation and yon obtain approxi- 



THE SURVEYOR'S GUIDE 13 

mate variation at the time survey was made. Reduce mag- 
netic bearings to true, set your vernier at present variation 
and run true bearings. 

A disputed line in the State of Connecticut was originally 
run on a bearing doubtful whether true bearings or magnetic; 
three surveyors obtained different results. Why? The vari- 
ation at the time the survey was made was unknown, and 
there was not sufficient data to be had to compute the correct 
annual increase. Each surveyor's computation differed, 
though approximately they agreed. 

Note — The result shows the importance of noting bearings 
true or magnetic, and noting correct variation at the time 
survey was made. 

To Reduce True Bearings to Magnetic. — Where vari- 
ation is east, add the variation to N. W. and S. E. bearings 
and subtract from the N. E. and S. W. bearings. 

When variation is west, add the variation to N. E. and S. 
W. bearings and subtract from N. W. and S. E. bearings. 

To Reduce Magnetic Bearings to True.— Where vari- 
ation is east, subtract the variation from N. W. and S. E. 
bearings and add the variation to N. E. and S. W. bearings. 

Where variation is west, subtract the variation from N. E. 
and S. W. bearings, and add variation to N. W. and S. E. 
bearings. 

To find the angles between two lines from the same 
corner : 

If the bearings of two lines close upon and start from the 
same corner, reverse the bearings of one of the lines and 
compute the angle as follows : 

Call N. and S. meridional letters. When the meridional 
letters are alike and the E. and W. unlike "the sum of the 
bearings is the angle." 

When the meridional letters are unlike and the E. or W. 
alike the angle is the sum of the bearings subtracted from 
i8o°. 

When the meridional letters are alike and the E. or W. 
alike, the angle is the difference of the bearings. 



14 THE SURVEYOR'S GUIDE 

When the meridional letters and the E. or W. are both 
unlike the difference of the bearings taken from 180 is the 
angle. 

Note — The surveyor should be very careful not to make 
mistakes in reversing the letters, for upon it depends a correct 
measurement of angles. 

EXAMPLES. 

Suppose the bearing of one of the courses is 

N. 17 25' W. reversed S. i7°25 / E. 

The other course is S. 16 30' W. 

Sum of bearings = 33 55 / the angle. 

Suppose the bearing is N. 30 40' E. 

Reverse the bearing S, 30 40' W. 

The other course N. 40 3c/ W. 

Sum of bearings 71 io / 

Taken from 180 

= Angle 108 5o / 

Suppose bearing is N. 25 2o / W. 

Reverse the bearing S. 25 20 / E. 

S. io° E. 

Difference of bearings 15 20 / the angle. 

vSuppose the reversed bearing is S, 40 io' E. 
The other bearing is N. 16 20' W. 

Difference 23 50' 

180 

Taken from 180 = 156 io' the angle. 



CHAPTER II. 

SUBDIVIDING AND DESCRIBING LANDS. 

One method is by metes and bounds ; the other by town- 
ships six miles square, subdivided into 36 sections approxi- 
mating one mile square. 

Note — Lands first enclosed in England, A. D. 842. 

* The first enactment in regard to surveying public lands was 
an ordinance passed by Congress May 20th, A. D. 1785, pre- 
scribing the mode of survey for the Western Territory and 
which provided that said territory should be divided into 
townships six miles square by lines running due north and 
south, and others crossing them at right angles as near as 
might be. It further provided that the first line running 
north and south should begin on the Ohio River at a point 
due north from the western terminus of a line run as a south 
boundary of the State of Pennsylvania, and the first line run- 
ning east and west should begin at the same point and extend 
through the whole territory. In these initial surveys only the 
exterior lines of the townships were surveyed, but the plats 
were marked by subdivisions into sections of one mile square 
numbered from 1 to 36, commencing with No. 1 in the south- 
east corner of the township and running from south to north 
in each tier to No. 36 in the northwest corner of the township. 
Mile corners were established on the township lines. 

The region embraced by the surveys under this law 

forms a part of the present State of Ohio and is generally 

known as "the Seven Ranges." See diagram Seven Ranges. 

The next act of Congress, approved May 18th, A. D. 1796, 

provides for the surveying of the territory northwest of the 

Ohio River and above the mouth of the Kentucky River. 

Section 2 of said act provided for dividing such lands as had 

not been already surveyed or disposed of, by north and south 

lines run according to the true meridian and by others 

crossing them at right angles, so as to form town- 

* Copied from a Pamphlet issued by the General Land Office in 
the year 1885. 

15 



1G THE SURVEYOR'S GUIDE 

DIAGRAM OF A TOWNSHIP— " THE SEVEN RANGES. 



36 


30 


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' 



Note. — Observe the method of numbering sections. Con- 
sidering the plan of subdividing a township, the numbering 
is more natural than the one subsequently adopted. 

DIAGRAM OF A TOWNSHIP N. W. TERRITORY. 



6 


5* 


4 


3 


Z 


, 


7 


8 


J 


10 


U 


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T, — N,, R. — E., 4th principal meridian. 
Note. — The north and west line of sections are fractional, 
but are shown in the diagram full sections. 



THE SURVEYOR'S GUIDE 17 

ships oi six miles square; it also provided that "one- 
half of said townships, taking them alternately, should be 
subdivided into sections containing as nearly as may be 640 
acres each, by running parallel lines through the same each 
way at the end of every two miles and marking a corner on 
each of said lines at the end of every mile." The act also 
provided that the sections shall be numbered respectively 
beginning with number one in the northeast section and 
proceeding west and east alternately through the township 
with progressive numbers till the thirty-sixth be completed. 
This method of numbering sections is still in use. See 
diagram. 

"The act of Congress approved February nth, 1805, directs 
the subdivision of the public lands into quarter sections and 
provides that all corners marked in the field shall be estab- 
lished as the proper corners of the sections or quarter sec- 
tions which they were intended to designate, and that corners 
of half and quarter sections not marked shall be placed as 
nearly as possible equidistant from those two corners which 
stand on the same line." This act further provides that " the 
boundary lines actually run and marked " (in the field) " shall 
be established as the proper boundary lines of the sections or 
subdivisions for which they were intended ; and the length 
of such lines as returned by the surveyors shall be held and 
considered the true length thereof, and the boundary lines 
which shall not have been actually ran and marked as aforesaid, 
shall be ascertained by running straight lines from the estab- 
lished corners to the opposite corresponding corners, but in 
those fractional townships where no such opposite or corre- 
sponding corners have been or can be fixed, the said boundary 
line shall be ascertained by running from the established corner 
due north and south, or east and west, as the case may be, to 
the external boundary of such fractional townships." 

Note — The foregoing acts of Congress are the principal 
acts controlling surveys in the Northwest Territory. 

From the foregoing synopsis of Congressional legislation 
it is evident : 



18 THE SURVEYOR'S GUIDE 

First. That the boundaries of the public lands estab- 
lished and returned by the duly appointed government 
surveyors when approved by the surveyor-general and 
accepted by the government are unchangeable. 

Second. That the original township, section and quarter 
section corners, established by the government surveyors 
must stand as the true corners which they were intended to 
represent, whether the corners be in place or not. 

Third. That quarter quarter corners not established by 
government surveyors must be planted equidistant and on 
line between the quarter section and section corner. 

Fourth. That all subdivisional lines of a section running 
between corners established in the original survey of a town- 
ship must be straight lines running from the proper corner in 
one exterior line to its opposite corresponding corner in tl^e 
opposite exterior line. 

Fifth. That in fractional sections when no opposite corre- 
sponding corner has been or can be established, any required 
subdivision line of such section must be run from the proper 
original corner in the boundary line due east and west, or 
north and south, as the case may be, to the water course, Indian 
reservation or other exterior boundary of such section. 



CHAPTER III. 

GEOGRAPHICAL POSITION OF MERIDIAN AND BASE 

LINES. 

A meridian line is a due north and south line. A base 
line is a line at right angles to meridian. 

tThe first principal meridian divides the States of Ohio 
and Indiana having for its initial base the Ohio River, and 
governs the surveys in the State of Ohio. This meridian is 
84 51' of longitude. 

*The second principal meridian starts from the confluence of 
the Little Blue River with the Ohio, runs north to the north- 
ern boundary of Indiana and governs the surveys in Indiana 
and a portion of those in Illinois. The meridian is 86° 28 / of 
longitude. 

Third principal meridian starts from the mouth of the Ohio 
River and extends to the northern boundary of the State of 
Illinois and governs the surveys in said state east of the 
meridian except those projected from the second meridian 
and the surveys on the west to the Illinois River. This 
meridian is 89 io 7 3o // of longitude. 

Fourth principal meridian starts in the middle of the 
channel of the mouth of the Illinois River, in latitude 38 58 / 
I2 // north and longitude 90 29/ 56" and extends north 
through Illinois, Wisconsin and northeastern Minnesota, and 
governs the surveys in Illinois west of the Illinois River, 
all the surveys in Wisconsin and that part of Minnnesota 
lying east of the Mississippi River and the third guide meri- 
dian (west of the fifth principal meridian) north of the river. 

* Note. — This meridian was the first one surveyed with scien- 
tific accuracy, A portion of the instruments used are now at 
West Point, in the philosophical department 0/ that institution, 

fAbbreviated copy of the Survey of Public Lands, issued by Gen- 
eral Land Commissioner. 

19 



20 THE SURVEYOR'S GUIDE 

The fifth principal meridian starts from the mouth of the 
Arkansas River and with a common base line running due 
west from the mouth of the St. Francis River in Arkansas 
governs the surveys in Arkansas, Missouri, Iowa and Minne- 
sota west of the Mississippi, and the third guide meridian 
north of the river, and in the Dakotas east of the Missouri 
River. This meridian is 90 58'' longitude. 

*The sixth principal meridian coincides with longitude 97 
22' and with the principal base line intersecting it on the 40th 
degree of north latitude, extends north to the intersection of 
the Missouri River and south to the 37th degree of north lati- 
tude, controlling the surveys in Kansas, Nebraska, that part 
of the Dakotas lying south and west of the Missouri River, 
Wyoming and Colorado, excepting the Valley of the Rio 
Grande. 

Michigan Meridian is in longitude 84 19/ 09", with a 
base line on a parallel seven miles north of Detroit. 

The Tallahassee Meridian is in longitude 84 i8 / , the start- 
ing point being the point of intersection with the base line 
at Tallahassee. It governs the surveys in Florida. 

The Saint Stephens Meridian starts from Mobile, crosses 
through Saint Stephens and intersects the base line on the 31st 
degree of north latitude. It controls the surveys of the south- 
ern district in Alabama and of the Pearl River district lying 
east of the river and south of Township 10 north, in the State 
of Mississippi. This meridian is longitude 88° o2 / '. 

The Huntsville Meridian, longitude 86° 31', extendsTrom 
the northern boundary of Alabama as a base, passes through 
the Town of Huntsville and governs the surveys of the north- 
ern district of Alabama. 

The Choctazv Meridian, longitude 89 io / 3o // , passes two 
miles west of the Town of Jackson, in the State of Missis- 
sippi, starting from a base line twenty-nine miles south of 
Jackson and terminating on the south boundary of the Chicka- 
saw Cession, controlling the surveys east and west of the 
meridian and north of the base. 

* " West from Greenwich " is omitted as it is understood west 
longitude. 



THE SURVEYOR'S GUIDE 21 

The Washington Meridian, longitude 91 05' ', seven miles 
east of the Town of Washington, in the State of Mississippi, 
with the base line corresponding with the 31st degree of 
north latitude, governs the surveys in the southwestern angle 
of the state. 

The Saint Helena Meridian, longitude 91 n / , extends 
from the 31st degree of north latitude as a base due south and 
passing one mile east of Baton Rouge, controls the surveys in 
the Greensburgh and the southeastern districts of Louisiana, 
both lying east of the Mississippi. 

The Louisiana Meridian, longitude 92 20 / ', intersects the 
31st degree north latitude, at a distance of forty-eight miles 
west of the eastern bank of the Mississippi River, and with 
the base line coincident with the said parallel of latitude, gov- 
erns the surveys in Louisiana west of the Mississippi. 

The New Mexico Meridian, longitude 106 52' 09", inter- 
sects the principal base line on the Rio Grande del Norte, 
about ten miles below the mouth of the Puerco River, on the 
parallel of 34 19' north latitude, and controls the surveys in 
New Mexico and in the Valley of the Rio Grande del Norte, 
in Colorado. 

The Great Salt Lake Meridian, longitude iii°53 / 47 // , 
intersects the base line at the corner of Temple Block, in Salt 
Lake City, Utah, on the parallel 40 46'' 04" north latitude, 
and governs the surveys in the Territory of Utah. 

The Boise Meridian, longitude 116 2o r , intersects the 
principal base between the Snake and Boise Rivers, in lati- 
tude 43 26' north. The initial monument is nineteen miles 
distant from Boise City on a course of south 29 3o / west. 
This meridian governs the surveys in the Territory of Idaho. 

The Mount Diablo Meridian, California, longitude 121 
54 / , intersects the base line on the summit of the mountain 
" Diablo," in latitude 37 53' north, and governs the surveys 
of all central and northeastern California, and the entire State 
of Nevada. 

The San Bernardino Meridian, California, longitude 116 
56', intersects the base line at Mount San Bernardino, lati- 



22 THE SURVEYOR'S GUIDE 

tude 34 o6 / north, and governs the surveys in southern Cali- 
fornia, lying east of the meridian, and that part of the 
surveys situated west of it which are south of the eighth 
standard parallel south of the Mount Diablo base line. 

The Humbolt Meridian, longitude 124 n / , intersects the 
principal base line on the summit of Mount Pierce, in latitude 
40 25' 30' north, and controls the surveys in the northwest- 
ern corner of California lying west of the coast range oi 
mountains and north of Township 5, south of Humboldt 
base. 

The Willamette Meridian, longitude 122 44', inter- 
sects the base line on the parallel of 45 30'' north latitude, 
and controls the surveys in Oregon and Washington. 

The Montana Meridian, longitude in° 40' 54 // , starts 
from an initial monument on the summit of a limestone hill, 
and extends north and south, the base line runs east and 
west from the monument on the parallel 45 36' 27 // north 
latitude. All the surveys of Montana are governed by this 
meridian. 

The Gila and Salt River Meridian intersects the base line 
on the south side of the Gila River opposite the mouth of 
Salt River in longitude 1 12° 15' 46" and latitude 33 22 r 57" 
north latitude, and governs the surveys in Arizona. 

The Indian Meridian intersects the base line at Fort 
Arbuckle, Indian Territory, in longitude 97 15' 56", lati- 
tude 34 3i / north, and governs the surveys in that territory. 

Standard parallel of latitude or correction lines are 
required every 24 miles, but generally the earlier surveys 
establish them 60 miles apart. 

Meridian and parallel lines are generally run with a solar 
compass or transit. The earlier surveys with a theodolite. 
CONVERGENCY OF RANGE LINE. 

The east and west township boundaries, called range lines, 
are supposed to have been run on a true meridian; hence it is 
clear that section lines, instead of being right parallels, con- 
verge, and the north boundary of a township is shorter than the 
south boundary, in proportion to their distance from the equator. 



THE SURVEYOR'S GUIDE 23 

It is necessary to correct this convergency by establish- 
ing a new base of 80 chains measurement to a section, every 
6d miles, called "correction parallels;" on these lines there 
is found two sets of corners, one set governing the closing cor- 
ners for the township south; the other set controlling surveys 
for the next 60 miles north. 

Government surveys now require guide meridians and 
parallels every 24 miles, which blocks the territory into tracts 
24 miles square. 

HOW TO OBTAIN LONGITUDE. 

A few geographical positions on the map of the public 
surveys being determined by astronomical observations, it 
is with little difficulty that the latitude and longitude of any 
place can be ascertained with precision. 

The longitude of a meridian being known, the longitude 
of a place can be approximately obtained, by taking from the 
column of difference of longitude the tabular number oppo- 
site the latitude, and multiplying it by the number of ranges 
the place is east or west of the meridian line; subtracting the 
product if east and adding if west. 

EXAMPLE. 

Milwaukee is in latitude 43 02'. 5, longitude 87 54' .2- 
The fourth principal meridian is longitude 90 3c/, and Mil- 
waukee is about 21^ ranges east of the meridian line. 

The tabular number is 7.1 X 21.5 —2° 33 / ; 90 30' 
— 2 33' — 87 57 / or 3' difference only, and close enough for 
the ordinary land surveyor in the performance of his work. 
HOW TO OBTAIN LATITUDE. 

The approximate latitude of a place can be obtained by the 
following rule : 

Take a point of known latitude; count the number of 
townships north or south and multiply by o° 5-i8 / ; the 
product added or subtracted to the known latitude will be the 
latitude sought. 

The south boundary of Wisconsin is latitude 42 30', 
required the latitude of Oshkosh, 17^ towns north, 17.25 



24 



THE SURVEYOR'S GUIDE 



X 5,18' '= i° 29' + 42 30' = 43 59', the latitude of 
Oshkosh. 

Lac du Flambeau is Ap.% towns north of the south bound- 
ary of Wisconsin, latitude 42 30'; 40^X5. 18' = 3 28 / + 
42 30 / = 45 58' latitude. 

Table of convergency of meridians six miles long and 
six miles apart; also difference of longitude per range. 






Co^Ver^e/ycy 


Difference df 
/.oHgiVtrt/e. per fo^ 


On the 








v* 


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UAra 


In Time 




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37 


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35 


J-*,? 


3-36 


6.5V 


ZS.HO 


36 


3U./ 


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6,40 


A 5.7/ 


37 


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3-55 


£.5o 


A 6.04 


33 


56.? 


V4 


6.60 


A 6. 31 


39 


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4.AA 


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A<f31 


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75, A 


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7-40 


19.9 A 


H7 


7 7.9 


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7. 6° 


30*7 


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80.6 


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7J0 


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£./-* 


X.oS 


3 A3 3 

I k 



Note. — Hipparchus locates the first degree of longitude atut 
latitude at Ferro. 



CHAPTER IV. 

SURVEY OF NORTHWEST TERRITORY. 

The Northwest Territory, according with act of congress, 
May 1 8th, 1796, is divided into townships, approximate to six 
miles square and are numbered north of a base line, and east 
or west of a true meridian line thus: 

*Town 22 North, in Range 6 east of the fourth principal 
meridian. 

tTownships are subdivided into thirty-six sections, approxi- 
mately one mile square, and described thus: Sec. 36, T. 22 
N., in R. 6 east of the fourth principal meridian. 

Sections are subdivided into quarter sections and described 
thus: The N. W. %, N. E. %, S. W. % or S. E. % of Sec. 
36, T. 22 N., in R. 6 east of the fourth principal meridian. 

Quarter sections are subdivided into quarters and 
described thus: The N. W. %, N. E. %, S. W. %, or S. E. 
X of the N. W. %, S. W. %, N. E. % or S. E. % of Sec. 
36, Town 22 N., in Range 6 east of the fourth principal meri- 
dian. 

This is the most perfect system of dividing and describing 
lands that can be devised, providing, however, the work is 
properly executed. 

All government surveys are made by contract by the mile. 
Hence the work is very imperfect. If the work had been 
properly executed there would not have been so large a differ- 
ence in the area of fractional sections on the north and west of 
a township, but each township would closely approximate six 
miles square, sections approximate close to one mile square, 
and fractional sections on the north and west of the township 
average an area nearer a full section. It is generally sup- 



*The first of these, it will be observed, is the system of rectangular 
co-orJinates. 

fThe second is the system of sections as the land is now sold by. 

25 



"26 THE SURVEYOR'S GUIDE 

posed that township lines are run with more care than section 
lines, but it is not a fact, l( contract work." The south line of 
Section 34, T. 23 N., R. 3 E. of the fourth principal meridian, 
is 6 rods, 22 links short.* 

Note. — Proportionate measurement applied, makes the 
government chain over two links short, an error too great to 
be consistent with accuracy or truth. 

The witness trees were all in place and agreed with gov- 
ernment field notes. The line was twice measured and the 
distance verified. It is plain that the entire system depends 
upon the chain, the compass is only auxiliary; hence the more 
uneven and brushy the surface the more imperfect the work. 
Seldom, if ever, do measurements agree with government field 
notes. More often measurements are less than those noted 
by government surveyors, specially on section lines crossing 
a meandered stream. 

METHOD OF SUBDIVIDING TOWNSHIPS. 

This plan of survey was devised by Col. Mansfield, then 
surveyor-general : 

A government surveyor goes to the S. E. corner of the 
township and obtains a true meridian or bearings of the range 
and township line boundaries of Sec. 36, he measures the 
length of boundaries for a base of operation; starting from 
the S. W. corner of Sec. 36, he runs north a line supposed to 
be parallel with the range line, and at 40 chains establishes 
the quarter post; at 40 chains more he establishes Sec. 
corner |||||, from thence he runs a random line east, parallel 
with the township line 40 chains, and temporarily sets the 
quarter post at a distance equal with his base (save his allow- 
ance of 80 links). He is supposed to intersect the N. E. corner 
of Sec. 36, but very seldom does. He corrects his course, and 
is supposed to run back, but instead reverses his notes and 
establishes the quarter post at a point equidistant between; 

*Probably the error occurred in crossing the Yellow River when 
at high stage of water. The quarter just stands on the west bank 
and the error is in the east half. Probably in triangulation across the 



THE SURVEYOR'S GUIDE 27 

he thus proceeds with the east tier of sections through to Sec. 
I, where all discrepancies in this tier have accumulated. He 
thus proceeds throughout the township to the west tier of 
sections, in which cumulative errors are thrust. 

It is evident such a method depends upon chaining.* 
Contracted by the mile through political influence, the sur- 
veys are rushed full of errors for future surveyors entangle- 
ment. After a lapse of fifty or more years, many witness 
trees and posts have rotted or burned and the original survey 
is completely obliterated. The surveyor is now confronted 
with serious original errors to re-establish a lost corner. 

The first surveys in the State of Michigan zvas so badly 
done that much oj it had to be resurveyed. The result has been 
two sets of field notes, a cause of endless trouble and dispute. 

Note. — By the term, lost corner, is one where the wit- 
ness trees and all evidence of its original locus is obliterated; 
existing conditions clearly comprehended, no surveyor can 
legally find the original locus of a lost comer. 

LOST CORNERS. 

First. We hold that it is impossible to retrace an errone- 
ous survey. 

Second. That there is no method at present by which you 
can locate a lost corner and swear it is the locus of the original 
That without a more definite law upon the subjeet no re-es- 
tablishment of a lost corner is arbitrary. 

Third. No arbitrary rule can be formulated which will be 
practical in general application. 

In the land office pamphlet to which we have before 
referred it, says: "The general rules herein given must be' 
considered merely as an expression of the opinion of this office 
on the subject; it is plain that extinct corners of the govern- 
ment surveys must be restored to their original locations 
whenever it is possible to do so; and hence resort should always 
be first had to the marks of the survey in the field. The locus 

*It is supposed that all interior section lines are parallel with the 
east and south lines of the township, which is far from fact. 



28 THE SURVEYOR'S GUIDE 

of the missing corner should be first identified on the ground 
by the aid of the mounds, pits, line trees, bearing trees, etc., 
described in the field notes of the original survey. The 
identification of mounds, pits and witness trees or other 
objects noted in the field notes of survey afford the best means 
of re-locatmg the missing corner in its original position.* If 
this cannot be done, clear and unquestioned testimony should 
be taken, if such can be at all obtained. In any event, whether 
the locus of the corner be fixed by the one means or the 
other, such locus should always be located and proven by 
measurements to known corners." 

Note. — This is using an error to prove something correct. 
It is a false theory, based upon presumption that the original 
measurements are absolutely correct. 

"No definite rules can be laid down as to what shall be 
sufficient evidence in such cases, and much must be left to the 
skill, fidetity and good judgment of the surveyor in the per- 
formance of his work." It further says: "Where difference 
in measurements occur, the surveyor must, in all cases, 
re-establish or prove his corners at intervals proportionate to 
those given in the field notes of the original survey; from this 
there can be no departure, since it is the basis upon which the 
whole operation depends for accuracy and truth." It is 
plainly evident that the general land office does not fully com- 
prehend the effect of proportionate measurements, but base a 
theory upon presumption that the original survey was correct; 
that the difference in measurements is caused by different 
lengths of chain; every practical surveyor has learned by 
experience that errors are too great to apply such a theory 
and approximate at all the original locus of a lost corner. 
That if he adopts the theory of proportionate measurements, 
the entire government survey in the township dependent upon 
said corner would be completely disarranged. 

*If such can be identified it is not a lost corner. 



CHAPTER V. 

ERRORS IN GOVERNMENT SURVEYS. 

One cause of error in government surveys is, "the great 
latitude given deputy surveyors in their instructions." 

First. Brush on or near the line are only required to be 
lopped and bent at right angles to the line by a blow of the 
axe at about the height of blazes. 

Note. — Every practical surveyor knows that correct chain- 
ing over such a line cannot be done. 

Second. The east and west section lines are allowed 
" eighty links " difference between actual distance established 
on the south boundary line of the township, and allowed 
" fifty links" to close north or south of a section corner. 
The north boundary and south boundary of any one section 
are allowed within "eighty links" of equal length. Mean- 
der lines are allowed five-eighths of a link for each chain, 
where the line is less than 80 chains long; where more than 80 
chains long he is allowed 150 links for closing error. 

It is evident the work must be very imperfectly performed 
not to be within required specifications; that the surveyor 
will take the full limit of 80 links in the performance of his 
work. The actual measurements are often 20 or more links 
less than government field notes, and the section line is 
actually one chain shorter than the south boundary of the 
township a base of measurement for that tier of sections in 
which the line is located. In theory he has run a line parallel 
with the range line, but practically it diverges or converges. 
WHAT SHOULD HAVE BEEN. 

Ten links ought to have been the extreme limit of differ- 
ence between the north line of a section and the south 
boundary line of the township in that tier. 

North and south lines of a section are positively instructed 
to be full 80 chains; yet they are often 40 or more links less, 
and unless there is an error in count, very seldom measure 

29 



30 



THE SURVEYOR'S GUIDE 



more. On east and west lines the surveyor takes his full limit 
of 80 links difference between the line and south boundary 
line of the township in that tier, and as the measurement is 
20 links less than actual, the line is one chain less than the base, 
" the south line of the township." These liberal instructions 
portend the trouble encountered in determining the locus of 
a lost corner. 

DIAGRAM OF A TOWNSHIP. 



Y 



W 













6 to 


fc 


5 


4 




* 6 


00 
- 1 ° 


Is 


6280 


5 7930 


7925 


7$ 2 3 


7921 


5 lozo 


7 


8 


9 


!0 


II 


I 12. 2 

«/ ° 


8l°>o 


7<m 


7930 


7<?5o 


7075 


■*- r<? 


16 


17 


/fo 


15 


14 


? 13 a 

Q c 


£3" + 


79?-/ 


79 f 


7430 


797-5 


5 79£o 


19 


20 


11 


Q.2 


23 


3 4-^ 


SJ*$ 


^30 


7930 


-'$40 


723o 


2- 7*2-5- 


30 


%<7 


18 


27 


2.6 




a 


#38* 


5 7HI 


4- 747-i. 


3 7*2-* 


2- 79ao 


/ 792-/ 


31 


32 


33 


34 


35f 






M 



T>t= ^ 5 R GL = P o "^ 

This township diagram is not drawn to a scale. 

Note. — Local attraction on the needle is a primary cause 
of divergence or convergence of north and south lines, chain- 
ing that of east and west lines, 

A TOWNSHIP VERY UNEVEN AND BRUSHY. 

(See Diagram.) 
A United States deputy surveyor runs north (supposed 
parallel with range line) from o to 1, thence a random line 
east, and at 79 chains 21 links intersects the range line 40 
links south of the section corner at M; as he is within the 
prescribed limit, at half the distance, 39 chains 60 links, in 
line between corners, he establishes the quarter post (a). 



THE SURVEYOR'S GUIDE 31 

As the random line is intended to be parallel with the south 
line (a town line) of the section, his chaining north is 40 links 
short of 80 chains. (A com m on error in a brushy or hilly 
country.) He then runs north on the same bearing, 80 
chains from i / to 2, thence a random line east, and at 79. 
chains 25 links intersects the range line 50 links south of the 
section corner at L, as he is within prescribed limits, at half 
the distance, 39 chains 62 links, in line between section cor- 
ners, he establishes the quarter post (b), his chaining north from 
I to 2 f is 10 links short of 80 chains, providing the sections 
are 80 chains on the range line; but this is not true, because 
there is often serious errors in town line measurements. 
From i' he runs north 80 chains to 3', thence a random line 
east, and at 79 chains 80 links intersects the range line 20 
links south of the section corner at K. But L to K measures 
40 links less than 80 chains. Consequently, from 2 / to 2> r 
the measurement is 10 links less than 80 chains. As he is 
within prescribed limits at half the distance, 39 chains 90 
links, between corners, he establishes the quarter post (r). 
From y he runs north 80 chains to \ r , thence a random line 
east, and at 80 chains intersects the range line 10 links south of 
section corner at I, but K I measures 10 links short of 80 
chains. The point of intersection, 10 links south of section 
corner I, is 319 chains 40 links north of the south boundary 
line of the township. The measurement from o to 4 / is 319- 
chains 40 links. Consequently, the chaining from 3 / to a/ is 
correct, but 4 / is 10 links south of a parallel line to intersect 
I. As he is within prescribed limits, at half the distance (40 
chains) between corners he establishes the quarter corner (d). 
From 4' he runs north 80 chains to 5', thence a random 
line east, and at 80 chains 20 links intersects the range line 
40 links south of section corner. The point of intersection on 
the range line, 40 links south of H, is 399 chains north of the 
south boundary and from o / to 5 it is 399 chains 40 links; 
consequently, from 4 to 5' the chaining is 40 links less than 
80 chains. As he is within prescribed limits in the perform- 
ance of his work, at half the distance, 40 chains 10 links, he 



32 



THE SURVEYOR'S GUIDE 



establishes quarter post (e); from o to 5 he is 1 chain short. 
From 5 he chains north 40 chains and sets temporary quar- 
ter post at (/"), thence north 41 chains and intersects the 
north boundary 40 links west of the section corner at F. As 
he is within prescribed limits he corrects his notes and may 
or may not (probably does not) change the quarter post at (/). 
While there are serious errors in chaining on north and 
south lines, there are greater ones on east and west lines. 
Observe the line M U from M on range line to No. 5 on the 
east line of west fractional sections. The notes are all within 
prescribed limit, and give to fractional section 31 on the noith 
boundary 3 chains 85 links more than properly belong to it. 
H Y, from H to 5, on the east line of west fractional section 7, 
throw to fraction 7, 2 chains 76 links. 

DIAGRAM OF TOWNSHIP 22 N., R. 4 E., 4th PRINCIPAL 

MERIDIAN. 



A 7°'° B 6VS C 73.0 £> 7V6 £. ,, 



F 7 vs G 



Y 



x 



w 



619 V 

-x £ >t> 
to b ^. 




«s 
5 *93 


i; 4 5 

V 6 


3 S°37 


K -2- e< 
X 7° 


0* 

S i*/7 


S3 73. 



7 •* 

' to 
9H9 


\* 

J" 833 


g/oo 
H b/x. 


8* 00 

JO 

3 *lt 


7<fOO 

x 7x9 


7? *o 

H Sir 


5ny 

9V3. 


8°1<> 

J- *l* 


$10 
H 7'7 


8/00 

/s 

3 rsf 


80HH 
x 8'° 


8100 
$ io* 


S6I7 

*> 
/? * 

t'7 


793/ 
*> 

5 8X7 


S09V 

A/ ^ 


8/00 

AA 

5 Bxo 


79 9* 

x, 807 


8100 


Z 811 


S78*> 

3o %. 
8/S 


7?X3 


3- 8/9 


79/7 

i y/s- 


fooo 
3 815 


79 0*/ 


X 806 


8100 
/ 7/3 


6IX0 

3/ V 

r 730 


790S 

Y 7*/S 


79/S- 

y its 


79 00 

3¥ 
y 80 


79/0 
7 7IO 


g/00 

^ 36 
y 70 


i 


5 


^ 


3, 7? 00 


7 79/o 


S 79 S6 



H 



THE SURVEYOR'S GUIDE 33 

The surveyor is not always within his prescribed distance 
of 80 links, as witness the diagram of Township 22 N., R. 4 
E. of the fourth principal meridian. The bearings and dis- 
tances are copied from an authenticated copy of the original 
survey. The distance is noted from 1 to M, 8[ chains. The 
west line of section 36 has a bearing i° 2. f greater than the 
east bearing, making the south boundary I chain 44 links less, 
= 79 chains 56 links; hence (1 to M) — (2 to L) — (3 to K) — 
(4 to I) all exceed prescribed limit of 80 links, 64 links. The 
east and west boundary line of section 35 are parallel sides' 
hence the length of the south boundary is 79 chains 10 links, 
2 7 to 3 exceeds the limit 2 links, 2' to 4 54 links. 

The east and west boundaries of section 34 are parallel; 
hence the length of the south boundary is 79 chains (on L V, 
3 to 2) exceeds the limit 20 links (on K W, 3 to 2), (I X, 3 to 
2), (H Y, 3 to 2), exceed prescribed limit 1 chain 20 links. 
The west line of section 33 is run on a variation 30' greater 
than the east side; hence it is safe to call the south bound- 
ary 79 chains 15 links for the length of the south boundary. 
(On K W, yt ' crg - ) exceeds the limit nearly 1 chain, (on I X, 
3^402), (on H Y, 3 to-2) exceeds the limit nearly 1 chain 5 
links. The west line of section 32 is run on a variation 15' 
greater than the east line; hence it is safe to call the length of 
the south boundary 79 chains 5 links. (On I X, 4 to~3.) ex- 
ceeds the limit 61 links, (on H Y, 4 to 3 ) exceeds the limit 1 
chain 15 links. The effect of such imperfect work is more 
clearly shown as follows: Computing the length of section 
lines from the east range line to the east line of fractional sec- 
tions on the west, we obtain the length of 

M 5, 397 chains 30 links, or 2 chains 70 links short of full. 
L 5, 398 "44 "1 " 56 " " " 

K 5, 402 " 17 " 2 " 17 " more than full. 

I 5, 403 " 90 " 3 " 90 " " " 

H 5, 401 " 80 " %/ " 80 " " 

From M to 5, we obtain a distance 397 chains 30 links 

" H to 5, " " « 401 " 80 

Difference.. 4 chains 50 links 



34 THE SURVEYOR'S GUIDE 

Computing distance by variation, we obtain a distance 
for the north and south boundaries of the township 

G to B 395 chains 89 links 

N to S 393 " 81 " 

Difference between the north and south 

boundary 2 chains 8 links 

Section 31 on the north boundary is les-s 

than it should have been 2 chains 7o links 

Section 30 is less-than it should have been 1 chain 56 links 
" I9"nwr«-than " " " 2 " 17 " 

a jC it it (C a a a ,, u „„ a 

it h it i< a it it a y a vJq 

The cause for so great difference in the area of fractional 
sections are hereby made clear. 

According with instructions issued by the general land 
office to deputy surveyors, the north and south lines are sup- 
posed to be parallel with the east range line, and east and 
west lines parallel with the south boundary line of the town- 
ship; but we have demonstrated very clearly that such condi- 
tions are adverse with facts. If it had been proven, the 
surveyor would have no trouble locating the original locus of 
a lost corner. 

How can we obtain the locus of a lost corner ? I believe 
it a correct principle, that the term " rectangular survey," 
imply "metes and bounds;" hence variation is a course and 
measurements the distance of a course given in the field notes 
of the subdivision of a township; the only difference, a tract 
is designated by numbers and infer boundaries. It is, there- 
fore, reasonable theory that each section in a sense is inde- 
pendent. 

Considering sections, rectangular tracts bounded by sec- 
tion lines, it is reasonable that the original variations given in 
field notes are the course of a line, and just as much a part of 
the survey as distance. Both must be practically applied. 
Theoretically it is the only data given to retrace original 
lines. 



THE SURVEYOR'S GUIDE 35- 

The following rules are based upon such a theory and 
must obtain more satisfactory results: 

Each section is independent of any other section in the 
township and must be governed by its marked and established 
boundaries. Should they be obliterated a last recourse must 
be had to the best evidence that can be obtained showing 
their former situation and place. Lenen vs. Smith, 7 Port. 
(Ala.), 42S. 

Note. — The theory of metes and bounds does not conflict 
with government surveys, theoretically it harmonizes with 
government instructions. Practically, if they do not corre- 
spond you are to determine which shall control. (See 
McCintock vs. Rogers, page 169.) Remember, you are not to 
locate a corner, but decide where it was. 

The rule that convinces the judgment most clearly is the 
one to apply. 

Surveyor-General to C. C. Palmer: "You will place the 
corner where the weight of evidence places it." 



CHAPTER VI. 

REQUIRED LOCUS OF LOST CORNERS. 

In the foregoing discussion it is evident the surveyor will 
be called upon to determine the following : 

First. The locus of a lost interior quarter section corner. 
Fig. i.. 

Second. The locus of a lost corner, on section lines clos- 
ing upon the north and west boundary of the township. Fig. 2. 

Third. The locus of quarter section common on township 
boundaries. Figs. 3-4. 

Fourth. The locus of interior section corners. Fig. 5. 

Fifth. The locus of closing section corners. Fig. 6. 

Sixth. The locus of section corners common to two town- 
ships. Fig. 7. 

Seventh. The locus of section corners common to four 
townships. Fig. 8. 

Eighth. The locus of a corner when a number of corners 
on all sides of the one sought are also lost. Fig. 9. 

Ninth. The locus of meander corners and lines. 

DIAGRAM OF LOST CORNERS. 



ft 



% 



Fig. I 



.*? 



? & 



F »£ * 






* § * fo ZO C * HO C <f 



^ 



Lost^< Sec/0 ot-osvfr 



«$ ■ * ■ — 4>j 



' J- 



r, a 




^t 



<£ 
^ 



»Sec. 6 



'ft 



> 



F.'6-3. 
7o»v/t - Has- 



39 90 <■ 3%#0 
" x o 

Sen 5 





Fi8 


+. 


< \ 




VH 





•< 


«sr«c 


30 



36 



THE SURVEYOR'S GUIDE 



37 



Kn-w-v 






.^ «o 



^ 



& 



f^Slio^^l^ 






Stz*l * 



^<See ^ 



FIG. 6. 



dW 




FIG. 7. 



Town Zi 


1?* E ^ t, 


80C 

Set y 

i ■ 


Y ?gC X9U ° 

/ «•* 

l> " Sec- 3 

> 



38 



THE SURVEYOR'S GUIDE 
FIG. 8. 



o 

36 s. 


%' 60 


TXXN %S 


t*zn %(> 


Y y°oo 


V /J© 


h 


/v 


5«C / «© 


h Sec 6 


•^ 




7 Zl N£?2 


Tzi N%b 



FIG. 9. 



6 


5 


1 


3 


z 


/ 


7 


8 


9 


/o 


// 


tz. 


/» 


'/ 


A6 * 

* * 

zi . 

Z8 ' 


/s- 

i * 

47 


M 


/3 


/? 


ZO * 
Zf ' 


Z3 


ZH 


30 


Z6 


zsr 


31 


3Z 


33 


3*f 


35 


36 



RE-ESTABLISHMENT OF LOST CORNERS. 

To establish a lost interior quarter section corner, when 
section corners are known but the quarter post between is 
lost. Fig. I. 

Run a straight line from section corner to section corner, 
and at a point in line equidistant between, locate the quarter 

post. 

Note. — Theoretically you have retraced the original line of 
•survey, and established the quarter post in its original locus. 
«' It is legally located." 



THE SURVEYOR'S GUIDE 39 

To re-establish a lost quarter corner on section lines closing 
upon the north and west boundaries of the township, when 
section corners are known but the quarter post between is 
lost. Fig. 2. 

Run a straight line from the south to the north section 
corner, or from the east section corner to the west section 
•corner, measure the distance, and at a proportionate distance 
given in the field notes establish the quarter post. 

Note. Theoretically you have retraced the original line, 
and established the quarter post in its original locus. "It is 
legally located." 

EXAMPLE. (See Fig. 2.) 

Suppose government field notes sets the north or west 
quarter post 40 chains north or west of a section corner, and 
at 20 chains more intersects the north or west section corner 
in township or range line; by actual measurement the total 
distance to township or range line is 59 chains or one chain 
short. 
60:40 :: 59: 39.32 >i 



. eg chains. 
60: 20 :: 59: 19.66^3 J 

Measure north or west 39 chains Z^Yz links, and in line 
between section corners establish quarter post. Note. — The 
location of fractional quarter posts by proportionate measure- 
ments are really the only conditions where proportionate 
measurements harmonize with the original survey. "The 
location is legal." 

To re-establish a lost quarter section corner on township 
boundaries, where the section corners are known. Figs. 3 
and 4. 

Note. — The east and west boundaries are range lines. 
The north and south are township lines. 

Run a straight line from section corner to section corner 
and equidistant between establish the quarter post. 

Note. — Theoretically you have retraced the original range 
and township line, and the quarter post is established in its 
original locus. "It is legally located." 

To re-establish a lost interior section corner where the north* 
south, east and west quarter posts are known, and govern- 
ment field notes give the variation of section lines. ' Fig. 5. 



40 THE SURVEYOR'S GUIDE 

Rule: Compute the variation of the needle at the time 
survey was made, the difference between that time and 
present will be your vernier reading; from the south quarter 
post run on government variation corrected to near the locus 
of the original corner and set temporary stake, thence north 
on government variation corrected to the north quarter post, 
if you intersect the post you have retraced the original 
section lines. From the west quarter post run east on govern- 
ment variation corrected to the temporary stake; thence on 
government variation corrected to the east quarter post; if 
you bisect the post; you have retraced the original section 
lines, and the temporary stake is the original locus (theoretic- 
ally) of the corner. If a transit instrument is used, and 
quarter corners can be seen from the section corner, compute 
deflection angle of the section lines, and set the instrument 
at a common point, where the angle of deflection will bisect 
the four quarter posts. Said point is the locus of the corner. 

Note. — Theoretically you have retraced the original section 
lines and the intersection point is the locus of the original 
corner. "It ought to be legally located." 

If government variations do not intersect the quarter posts 
they are erroneous, and the corner can be located according 
with the following instructions on restoration of lost corners 
found in the land office circular to which we have before referred. 
In the absence of sight trees and other evidence regarding the 
line, as in an open country, or when such evidence has been 
destroyed by time, the elements or. the progress of improve 
ment, the line connecting known corners should be run 
straight from corner to corner. 

Note. — This harmonizes with the original intent of the 

survey; which provides that north and south lines are to be 

run a line meridian, and east and west lines cross them at 

right angles near as may be, the point of intersection is the 

locus of a section corner. 

EXAMPLE. (Fig. 5.) 

From quarter post C to section corner by Gov. is 40 chains. 
" section corner to % post A " " " 40 " 

" quarter post B to section corner " " " 39. 90 " 
" " " D to section corner " " "39.80" 



THE SURVEYOR'S GUIDE 41 

By actual measurement, the distance C to A is 79 chains, 
or one chain short of government notes. From B to U it is 
80 chains or 30 links more than government notes; which 
side of the section corner is the error? 

It is evident that proportionate measurements will notlocate 
it in harmony with the original or with a theory. That govern- 
ment lines are run due north and south and east and west, by 
lines parallel with the east and south line of the township. 

To establish closing section corners where the N,, S., E. and 
W. quarter corners are known; closing section corners are 
on the range line, hence the west tier of sections are frac- 
tional. Fig. 6. 

Rule: From the south quarter post run a straight line to 
the north quarter post, and you theoretically retrace the 
range line. Go to the east quarter post, compute the variation 
and run west to the range line, and set temporary post, go to 
the west quarter post, compute the variation and run east; if 
you bisect the temporary post, you have found the locus of 
the section corner. If you do not bisect compute the latitude 
and departure, and re-run the line. The point of intersection 
on the range line is (theoretically) the locus of the original 
corner. "It ought be legally located." 

Note. — The subdividing of separate townships are inde- 
pendent, surveys independent of each other, hence propor- 
tionate measurements cannot be used in locating a corner on 
range lines. Theoretically, by the above rule, you have 
retraced the original section and range lines, and obtained the 
original locus of the section corner. It may be objected that 
noted variations are more liable to error than measurements; 
unless there is local attraction it is not a fact with corrected 
variation of closing lines. 

EXAMPLE. 

In the year 185 1, latitude 44 30', longitude 90 30' W., 
Township 22, R. 6 E., was subdivided. In 1894 the 
S, W. corner of section 18 in a range line is a lost 
corner. The S, % post in the Wisconsin River, 
the west ]^ post lost, the west ^ post of section 19 in 
the Wisconsin River, the south % post of section 13 lost; the 



42 THE SURVEYOR'S GUIDE 

S. W. and N, W, corner section 13 known. The S. E. corner 
of section 18 was established in 1873 and designated by a 
stone monument, distant west from the S. E. known section 
corner of 17 = 80 chains. The S, W, corner of section 19 is 
lost. The distance south from the S, W, corner of section 18 
to the Wisconsin River is eleven chains. The distance given 
in the field notes from the S. W. corner of section 13 to the 
S. W. corner of section 18 is 79 chains 70 links. The distance 
given on the south line of section 18 is 69 chains 59 links. 
The variations are noted by government. After deliberating 
upon a method, the following was adopted: Measured from 
the S. E. corner of section 18 to the S. W. corner of section 13, 
and ascertained distance one chain more than govern- 
ment notes. From the S. W. corner of section 13 run the line 
■east on a corrected variation and measured the distance 79 
chains 70 links, and set temporary post. From the N. E. 
corner of section 18 run south on range line on a corrected 
variation, and bisected the temporary post 42 links short of 
one mile or of 80 chains. (Note. — This difference of 42 links 
between actual measurement and supposed measurement of 
80 chains on a range line, and a difference of one chain from the 
S. E. corner of section 18 to the S. W. corner of section 13 shows 
very careless original work. A flagstaff at the S. E. corner 
of section 18 was prominently visible from the S. W. corner. 
Set the variation and brought the instrument into line bisect- 
ing the range line close to the temporary post established it 
the locus of the original corner.) 

Measured across the river from S. E. corner of section 18, 
and found the error was made in crossing the river, suppose 
proportionate measurements had been adopted, it would 
locate the corner two rods east of the. range line, and is not 
in harmony with the original survey. 

To re-establish section corners common to two townships 
when the E., W., N. and S. quarter are known. (Note. — 
Township boundaries are the north and south lines of a town- 
ship, consequently the north tier of sections are fractional. ) 
Fig. 7- 



THE SURVEYOR'S GUIDE 43 

Rule: From the west quarter post run a straight line to the 
east quarter post, and theoretically you retrace the original 
township line. Go to the north quarter post, compute the 
variation, and run south to the town line; go to the south 
quarter post, compute the variation, run north, and if you 
bisect the temporary post you have theoretically obtained the 
locus of the lost corner. 

Note. — Theoretically you have run the original section lines. 

To re-establish section corners common to lour townships 
where quarter corners N., S., E. and W. are known. Fig. 8. 
Rule: Go to the south quarter post, compute the varia- 
tion and run north the given number of chains and set 
temporary post. Compute the variation and runthence north 
to the north quarter post; if you bisect the post you have 
retraced the original lines. Go east, compute variation and 
run west; if you. bisect the temporary post you have proba- 
bly found the locus of the corner. Go west, compute the 
variation and run east; if you bisect the temporary post 
you verify the locus of the corner. If neither lines bisect, 
correct latitude and departure and re-run the lines; the inter- 
section point of said corrected lines is the locus of the corner. 

Note. — Theoretically you have retraced the original town- 
ship lines, and the locus of the corner in original place. No 
plan of measurement can locate the corner so close to the 
original as the above rule, but the one may serve a rough 
check upon the other. 

To re-establish a lost corner where a number of corners on 
all sides of the one sought are also lost. Fig. 9. 

We are now confronted with a more difficult problem. 
The land office on this question still adheres to a false theory 
of proportionate measurements. 

Substantially the conditions are the same as an unsubdi- 
vided township and the same method of survey is applicable. 
See Fig. 9. 

Commence at the S. W. corner of section 26 and obtain 
the bearing of the west line of said section and set your ver- 
nier. From section corner |||f J run north 40 chains and set 



44 THE SURVEYOR'S GUIDE 

a temporary % post, thence 40 chains more set temporary 
section corner ||||f ; thence run east parallel with the south 
line of section 27 (bearing having been previously obtained) 
40 chains, and set temporary ^ post, thence 40 chains more. 
You are supposed to intersect section corner |f |||. If you do not, 
enter in your field books the proper notes. At said section corner, 
ascertain the bearing of the west line of section 23. Return 
to section corner §£'§§■ and run north 40 chains and set tem- 
porary ^ post, kX. 40 chains more set temporary section cor- 
ner |f|l$§; run thence east parallel with the north line oi 
section 34, 40 chains, and set temporary ^ post. At 40 chains 
more you are supposed to intersect section corner \\ |||. If 
you do not, enter the proper notes in your field book. At said 
section corner obtain the bearing of the west line of section 14. 
Return to section corner ^|j^|and run north 40 chains and set 
temporary % post. At 40 chains more you are supposed to inter- 
sect section corner r 9 gir|. If you do not, enter the proper notes in 
your field book. Now, go to section corner |||||, run north 
40 chains and set temporary % post; thence 40 chains more 
and set temporary section corner |f|||, thence run east 40 
chains and set temporary % post; thence east parallel with 
the north line of section 33 (bearing having been previously 
obtained), 40 chains more. If you do not intersect temporary 
section corner |^[|f make the proper notes in your field book. 
Return to section corner |f||^. Thence run west, parallel 
with the north line of section 32, 40 chains and set temporary 
% corner. At 40 chains more you are supposed to intersect 
section corner ^i|§. If you do not, enter in field book the 
proper notes. Obtain the bearing of the west line of sections 
29 and 20 and enter it in field book. Return to section cor- 
ner ff jfg-; run thence north 40 chains and set temporary 
quarter corner, thence north 40 chains more, where you are 
supposed to intersect section corner |-gj||. If you do not, 
enter the proper notes in your field book. Obtain the bear- 
ings of the south line of sections 17-9 and 10, and enter them 
in field book. You have now obtained sufficient data by which 
you can make proper corrections for permanently establishing 



THE SURVEYOR'S GUIDE 45 

the locus of the lost corner. Theoretically you have retraced 

the original survey. 

Suppose in measuring north from section corner ||||| to 

section corner -^\%, supposed to be 240 chains, you found it 

2 chains short; where was the error made? Suppose in 

measuring west from section corner |f||f to section corner 

rolfir> y ou nn d the measurement 1 chain less than the original 

noted at 239 chains; where was the error made ? The above 

method may possibly locate the error. 

Note — Expense may be objectionable to this plan of survey; 
but as it is strictly in accord with the original plan, it is the 
only legal one to adopt. 

RE-ESTABLISHMENT OF MEANDER CORNERS AND 
MEANDERS. 

Again, the rule of government land office is based upon a 
false premise that the measurements made by government 
surveyors are correct. It says before proceeding with the 
establishment of missing meander corners, the surveyor will 
carefully rechain at least three of the section lines between 
known corners of the township within which the lost corner is 
to be re-located, in order to establish the proportionate meas- 
urement to be used. 

Note. — A theory not practical because it presumes a differ- 
ence in length of chain instead of errors too great for obtaining 
proportionate ?neasurements, as every practical surveyor knows. 

*TO RETRACE ORIGINAL MEANDER LINES. 

"The variation of the needle as noted is not to be 
implicitly depended upon, since the observations for varia- 
tion are, in many instances, crude and rough, and at best 
afford only an approximate in such work; it is preferable when 
such variation has been carefully noted (seldom done) in the 
original field notes of survey and the lines have been run 
with a true meridian throughout (not probable) to retrace 
the meanders by the angles made by the several successive 
courses." 

Note. — This is preferable, providing there are no errors in 
courses. Suppose there is an error in the first course, the error 
will then be carried throughotit the meandered line. However, 
if this was the only error the angles can be corrected by latitude 
and departure. 

*Land office pamphlet, 1885. 



46 THE SURVEYOR'S GUIDE 

To retrace a meandered line and obtain original cannot be 
done. The errors in original work are such that no surveyor 
can swear he has located the origiual line, but may believe 
his work closely approximates. The deputy is allowed where 
the line is over 80 chains 150 links for closing error. It is 
clear, that with this very liberal allowance, no dependence 
can be placed in the field notes of a meandered line; proba- 
bly the closest approximate can be obtained by measuring the 
angles and correcting latitude and departure. 

As an example, Sec. 18, T. 22, R. 61, through which runs 
the Wisconsin River. Section lines differ from government 
notes from 40 links to 1 chain. The folly of obtaining pro- 
portionate measurements to be used on meandered lines is 
clearly apparent. 

Meandered corners on a stream similar with the Wiscon- 
sin, are soon obliterated; in many instances the banks have 
washed so the original locus is now in the river. How can 
they be restored ? Different conditions will require different 
methods. The surveyor must rely upon judgment, and apply 
the one which will in theory approximate closest the original 
corner. Take the south line of Sec. 18; we have discovered 
an error of I chain in crossing the river. The only method is 
to measure in accord with government notes from the south- 
east corner of Sec. 18 to the supposed locus, now in the river. 

Measure from the southwest corner of Sec. 18 east in 
accord with government notes to the supposed locus of the 
original, now in the river. 

It is evident that proportionate measurements applied to 
locating lost meander posts in Sec. 18, will be far from 
approximating the original locus of the corner. 

Proceeding down stream, the bank on the left hand is 
termed the "left bank," and that on the right the "right 
bank," and are used to distinguish the two banks of a stream. 

Streams, whether declared navigable or not, are not 
meandered above a point where the average right angle width 
is less than 3 chains. 

The distance between meander corners on some line is 
ascertained by triangulation*, where direct measurement 

*Distance by triangulation when done with a compass is often 
incorrect. 



THE SURVEYOR'S GUIDE 



47 



is not practicable, and when the distance is more than 10 
chains, whole chains only are taken, when less, the number 
of links is a multiple often. 

TO LOCATE A CORNER BY WITNESS TREES. 

The bearing to witness trees should have been taken true 
meridian, but they are not probably so taken, but on a 
variation noted on the line run; thus if the variation of a line 
is noted g° the bearing to witness trees are taken with the 
vernier set at 9 . 

Rule: Compute the difference in variation between the 
time of survey and present time and subtract it from varia- 
tion of the line off which witness trees were located. Set your 
vernier and use original bearings. 

We are again confronted with serious errors in bearings 

and distances. The surveyor was in too great rush to take 

time for the needle to settle, and when vibrating, estimates the 

reading. In like careless manner the chainmen rush the 

chain through brush, and consequently bearings and distances 

seldom agree. 

EXAMPLE. 

Suppose the bearing to one of the trees is N. io°, E. 60 

links, and to the other S. 8o°, W. 75 links (see diagram) the 

included angle A B C = no°, measured side A B = no 

links. We now have three sides, only one of which, A B, is 

positively known to hnd the other parts. 

FIG. I. FIG. 2. 

J/ #> 




Bearings accepted correct. Distance accepted correct. 



48 THE SURVEYOR'S GUIDE 

Set instrument at C and from off A to B measured the 
angle no°, measured the side A C and B C and found they 
did not agree with bearings. The error is either in bearings 
or distances. 

If the error be in distance and bearings are correct, we 
obtain the included angle A C B, Fig. i = no°, angle C A 
B = 39° 27', angle A B C = 30 33'. To find B C no° : 
39 27/ : no: BC = 74.38. 

To find AC 110 : 30 33 / :: no : A C = 59.50. If the 
error be in bearings, to compute the angles B A C and A B 
C, we have the side A B as a base no links .-. as the base 
no is to the sum of the two other sides so is the difference of 
the sides to the segment of the base. 

no : 60 + 75 = 135 :: 75 — 60= 15 : ii^ 4 - 1 = 9.205. Half 
the base = 55 — half the difference 9.205 =45.795 = short 
segment half the base — 55 + half the difference — 64,205 long 
segment ^^ 9 - 5 = co-sine B A C = 40 15' -S^-^os = co-sine A B 
C = 31 07' ; 1 io° + 40 I5 r + 31 oj / — 181 22 7 , an error 
of i° 22 r ; hence there is an error of 4s 7 in bearing C A and 
34' in bearing C B. The bearing C A is N. 9 12' E., C B 
S. 8o° 34 / W., and the included angle A C B ro8° 38'. 

As the error in distance is less than one link assume bear- 
ings correct and point C the locus of the corner. 

It is evident there is no method which will determine 
whether the error is in distance or bearing. The surveyor 
must depend upon judgment. 

Proportionate measurements will not harmonize with the 
original survey when serious original errors were made in the 
survey of toivnship lines. 

Take the south line of Sec. 34, T. 23 N., R. 3 E., to which 
we have before referrred. The United States deputy surveyor 
discovered in measuring west from the S. E. corner of Sec. 34 
that the section is 6 R. 22 links short; but not having authority 
to change it, he probably computes a bearing which will at 80 
chains north locate section corner ff|f£ 80 chains west of sec- 
tion corner JJiff and should note it in his field book. 



THE S UR VE YOK* S G UIDE 49 

The deputy has established the west quarter post of Sec. 
3, T. 22 N., R, 3 E,, 40 chains north of section corner f j^ and 
in a line supposed to be parallel with the east range line; he 
continues the same course north to the town line and finds he 
is 6 R. 22 links west of section corner 3 /| 3 /. He is supposed 
to compute a bearing which will run a straight line from the S, 
W. corner to the N. W. corner of Sec. 3, and should enter it in 
his field book; but more than probable he does not change the 
quarter post, or enter the proper notes in his field book. If he 
does not, you have no data controlling the locu s oi the corner, and 
the only recourse left is equidistance between the N. E, cor- 
ner of Sec. 3 and N. W, corner of Sec. 4. If he did enter the 
proper notes, correct the variation and proceed as with the 
rule re-establishing a corner common to two townships. 

It may be readily observed, that in this case, proportionate 
measurements locate the corner 3 rods and 11 links west of 
the original; that the only recourse to restore it to its original 
place is in a proper entry of the original notes of the survey. 

The re-establishment of a lost corner depends upon the 
skill and judgment of the surveyor. He may locate a lost 
corner satisfactory to one party and unsatisfactory to the other. 
His corner is correct, but the dissatisfied party employs 
another surveyor, who, perchance, locates it satisfactory to 
him, and unsatisfactory to the other. Neither are now satis- 
fied, and the locus of the corner becomes a bone of contention. 
The county surveyor (perhaps a man of very ordinary intelli- 
gence) is called upon under the impression the locus of his 
corner and work is legal, and precedently so far as it requires 
proof of an error, it is. He differs from the other surveyors, 
and we have three surveyors differing in results. It is not 
an exceptional case when two surveyors and a county surveyor 
differ in the locus of a lost corner. Why ? Surveyors are 
not firmly impressed with the importance of maintaining a 
standard length of chain. Consequently there is a difference 
in the chaining. Let us examine. Suppose the chain is one 
inch too long ('not uncommon); 80 chains measures 10 links 
more than one mile, if ]/ 2 inch too long, 80 chains measures 5 



50 THE SURVEYOR'S GUIDE 

links over one m ile, and this error may be augmented by thought- 
lessly using wooden tally pins from^ inch to )/ 2 inch in diameter,, 
making an excess per chain equal to the diameter of the pin. 
Suppose the chain is I inch too long and tally pins y z inch 
in diameter, 80 chains measure 15 links over one mile. If 
chain be % inch too long and tally pins ^ inch in 
diameter, 80 chains measure 5 links over one mile. Such 
conditions are by no means an uncommon occurrence. 
Observe that these little matters, regarded of small conse- 
quence, in the aggregate are serious in their application. 

Again, chaining is too often trusted with those whose 
knowledge of the important part of their work is limited to 
dragging the chain. The same chainmen chaining over the 
same ground twice seldom obtain the same result. 

Another source of error "an obstructed line in brush," 
through which correct chaining cannot be done. Another 
cause of error, "incomprehension of correct variation," 
Without such knowledge the surveyor cannot do correct work.. 
Suppose you are running on an error of 15' only, the departure 
is 23 feet per mile. Another cause of error " the surveyor is 
too often impressed, land is of little value." The work is 
done in the same careless manner as was the original, and 
hurried through without giving it the necessary time to do 
correct work. 

Note, — The surveyor has no right to consider value. It 
is of no account with him whether land is worth 100 cents or 
$100 per acre. He is not only doing work to accommodate 
the present but a future. 

Land at the time of government survey was worth i^^ 
dollars per acre. This nominal value was the controlling 
principle in the work. And, to-day, less than fifty years, 
disputed corners has forced many into costly litigation. The 
same principle controlled the subdividing ot sections, and, 
to-day, many residents of villages and cities are at sea with 
deeds. 

The chain or tape is an important factor in a correct sur- 
vey, and the surveyor cannot be overzealous in his instruc- 



4 


feet in i 


6 


it T 


8 


(< I 


10 


" T 


12 


«( T 


14 


it J 


20 


" T 


26 

33 


(( T 
'* I 



7Wi? SURVEYOR'S GUIDE 51 

tions to chainmen. He should observe that the head chain- 
man draws his chain straight, and taut, and properly sticks 
his pin at the exact point. Measurements in common sur- 
veying conform with the surface, but when slopes intervene of 
chain add ^ links,. 

< < a 4_ 1 1 

10 
a a 3 a 

4 

1 10 
a ti f 6 << 

" « /l 6_ << 

H-l 6 
(< <« g << 

(( ( . T -. i l( 

1 OI 

With the majority of chainmen you will obtain closer work 
with uniform surface measurement than attempting to hold 
the chain level. 

PRELIMINARY WORK LOCATING A LOST CORNER. 

Whenever a surveyor is called upon to locate a lost corner 
he should obtain the full and complete field notes of the town- 
ship, and on the ground study the situation, then by measure- 
ments and running of lines he may determine where the 
errors (if any have developed) occurred, after accomplishing 
preliminary work he may be able to apply a method which 
may locate the corner approximating the original. 

Without sufficient preliminary work you cannot determine 
upon an approximate locus of a corner. 

There has been a careless, yea, criminal, destruction of 
witness trees, line trees, and other evidence of government 
surveys, which together with fire has completed the work of 
destruction, obliterating all trace of the original survey. 
Hence there is so much doubt connected with the survey of a 
disputed line, that statute of limitation is a point well chosen 
in litigation. 

From the foregoing discussion of lost corners the locus of 
quarter posts between two adjacent section corners, are the 
only corners wherein is undoubtedly obtained a legal re-estab- 
lishment. 



52 THE SURVEYOR'S GUIDE 

In 1873, twenty-one years ago, a section was subdivided and 
the section corners, quarter corners, and eighth corners desig- 
nated by permanent stone monuments. They ought now to 
be recognized legal corners, especially so, when the work of 
subdivision is as near correct as can be obtained. In the year 
1890 a surveyor intended to run a quarter line east, parallel 
with the north line of the section, to a meandered stream, 
where the line ended; probably adopting a theory that frac- 
tional lines of a section upon one side of a meandered stream 
are independent of the other side. (See page — . ) This line 
was prolonged across the river and intersected the section line 
52 feet south of the % post designated by a stone monument, 
being one of the corners mentioned in the above subdivided 
.section. 

There was no positive evidence that the west quarter post 
was the locus of the original post. The east quarter post was 
re-established in 1892 in a straight line produced from the 
Y% post equidistant that to section corner, and is located 
approximately near that of 1873. 

A tract of land was conveyed a given number of chains 
wide, and the north boundary line described a given number 
of chains north of the west quarter post, and extending east 
parallel with the quarter line above mentioned. It is plain, 
the north boundary line of said tract depends upon a correct 
quarter line depending upon a correct locus of the quarter post. 

Assuming the quarter line correctly located, it locates 
the north boundary line of the above described tract 
north of the present fence line. A writ of eject- 
ment was served upon the alleged tresspasser, the 
defense plead statute of limitation, and the jury decided 
no cause of action. The plaintiff is still dispossessed of his 
complement of land. This case is referred to as one of those 
very difficult ones, to determine the legal locus of a doubtful 
corner, and suggests: How can a lost corner be legally 
re-established unquestionable in court ? 

A suggestion pass a law, and let the proper constituted 
authority appoint a competent state engineer to investigate 



THE SURVEYOR'S GUIDE 53 

the work of a surveyor, whenever called upon so to 
do, and upon thorough investigation he finds the work 
properly executed, his decision shall be legal and final, and 
binding upon the interested parties. The expense of such 
arbitration would be much less than unsatisfactory litigation. 
Whenever a corner is positively known as the locus of the 
original, it is unaccountable that parties bounded by such 
corner are not sufficiently interested to preserve it with a 
suitable stone monument. 

EXPENSE OF SURVEY. 

An individual desires a forty located, which cannot be 
done unless the section is legally subdivided; he is compelled 
to pay the total expense. (Note. — There ought to be a law 
passed compelling all parties bounded by a corner to defray their 
proportionate part of the expense. ) He has no conception of the 
work or time required, in subdividing a section, to obtain a 
legal survey (neither can the surveyor tell him). It seems to 
him very simple to run a line, stick a stake, and c\\\ it the 
corner Very naturally, he believes a surveyor is taking 
unnecessary time; nevertheless, the surveyor should take 
sufficient time to do correct work, and as he is the only 
competent judge, take all necessary time to satisfy himself 
that he has made a correct survey, or obtained an approximate 
locus of a corner. 



CHAPTER VII. 

SUBDIVIDING SECTIONS. 

To subdivide a section into quarter sections, run straight 
lines from the quarter post on one side to the corresponding 
quarter post on the opposite side, and at the point of inter- 
section of the lines set the center quarter section post. "This 
unethod is recognized as legal." 

To subdivide a quarter section into sixteenths run straight 
lines from post to post on all sides of the quarter section, and 
at a point in line equidistant between, set */g posts. Run 
straight lines from one exterior y% post to the corresponding 
• opposite exterior )/% post, and at the intersection point of the 
lines set the Jg- post. "This method is legal." Apply the 
.same method for smaller subdivisions, and the section will 
have been legally subdivided. 

Apply the same method of subdividing fractions on the 
north and west of a township. 

To subdivide fractional sections bounded on one or more 
sides by a meandered stream or lake. These subdivisions are 
supposed to have been surveyed in the field by government 
surveyors, they are not, but are platted and computed in the 
office, hence are liable to serious error. 

The only lines run by government surveyors are the exterior 
lines of a section, and the courses and distances on the bank 
of a stream or lake between meander posts set in section lines 
only. The same rule as the one applied to other sections 
applies to fractional sections, except a lake or stream takes 
from the section the amount enclosed between meander lines. 
Refer to government plat and subdivide approximately as 
platted, using so far as practicable the rule for subdividing a 
section. 

CORRECTING DEPARTURE. 

In running a straight line toward a post or corner it is very 
seldom bisected, but comes out at the right or left of the 
post at B 

54 



THE SURVEYOR'S GUIDE 55 

From oft the line run, measure a right angle and distance 
to the post C The length of line to said point B is the 
latitude and distance from said point B to the point C 
the departure. Multiply departure by 57-3°, and divide 
product by the latitude, the quotient will be the angle of 
correction. 

Note. — This will approximate very closely not to exceed 
one-twentieth of the latitude and is based upon similiar 
triangles, thus a 1° curve is 5730 feet radius, the tangent, for 
1° being 100 feet, the tangent of 1° for 1 foot is a radius 
fou °f 573° = 57-3» Change the denomination to degrees = 

j/10 • 

EXAMPLES. 

Suppose you have run a line 8d chains on a variation of 9 , 

and at right angles you are at the right of the post I chain 

.40 links. 

1 chain 40 links x 57. 3 Q 

80 chains. 

Note. — The quotient will be in degrees and decimal of 

degree. Multiply decimal by 6o / point off two places for 

minutes. 

Set your venier at io° and re-run the line. ''Change your 

chain measurement to links." 

Suppose you had come out 50 links to the left of C; 

57.3 x,5Q = o 2I /. 

80 
•9 — o°2i / =8° 39/ to set your vernier. 

By trigonometrical formulae: 

Divide departure C B by latitude A B; the quotient will 
be natural tangent. 
I ch. 40 links = .01746 = tan. i°. fg = natural tangent = 

8o~ 
.00625 =°° 2j/ nearly, "Always observe decimal places in 

your computation." 

BY OFFSETS 

As the distance run, or latitude A B is to the distance to 

the post, or departure C B, so is a distance. A D to the 

required offset D E. 

EXAMPLE. 

As 80 chains : I chain 40 links : : 40 chains to the required 

offset 70 links D E to set % post, remembering offsets are to 

be measured at right angles to the line run, or, in other 

words, to the latitude. 



DIAGRAM. 



C B is the de- 
parture. 

A B is the lati- 
tude. 

CB 
A B 
BA C. 



= tan. 



T^e 

'^^i' 



'^7 ^ 



?0L 



"tf 



00 






You will sel- 
dom exceed 50 
links of de- 
parture, If 
you do not, 
the difference 
in lines A C 
and A B is so 
small that 
practically 
there is no dif- 
ference. 



'«<*/© 



t c 



°^ t 



CHAPTER VIII, 

The subject oflost corners has been fully discussed in the 
foregoing chapters, and errors pertaining to government sur- 
veys clearly demonstrated; following in order is the discus- 
sion of 

MISSING CORNERS. 

By the term missing corner is one where there can be 
obtained more or less evidence of its original locus, 

A successful tracing of such evidence depends upon the 
tact and observing talent of the surveyor. One surveyor may 
possess these faculties in a high degree and another has none 
at all. 

Note. — There is a class of woodsmen called "timber esti- 
maters," who are experts in finding missing corners; relying 
more upon physical investigation, they are often more suc- 
cessful in this line than the favored, skilled engineer. Out 
of this class in a timbered country, are chosen many county 
surveyors. Some of them have only a limited arithmetical 
knowledge, yet, practically, in ordinary land surveying are 
just as skillful as the more favored, educated engineer. But 
it is no argument against science. It simply demonstrates 
that observation and tact can be more successful in this line 
than the scientific engineer lacking this special talent. 

First. We have the stumps of witness trees in many 
instances almost entirely obliterated by rot. The surveyor 
checks upon them according with field notes and practically 
finds them in harmony. For further evidence he examines the 
wood and decides it is the same kind of tree as described in 
field notes. He finds corroborate evidence in the testimony 
of living witnesses, and then locates the corner according to 
the bearings and distances given in the field notes, all of 
which he records in his field book for future reference. 

Second, He finds witness trees obliterated. 

By observation and experimental measurements he deter- 
mines about where to look for the bottom of the stake. If in 

57 



58 THE SURVEYOR'S GUIDE 

sand soil, with a hoe, he easily and quickly scrapes off the 
soil, and is often successful in his search. If the stake is 
entirely rotted, the discoloration of the sand soil will be 
similar in shape as the original stake. If the soil is stiff clay, 
the chances are the bottom of the stake is still preserved. If 
decayed, you may often find a hole the size and shape of the 
stake, or, if partially filled, a pin may readily be thrust to the 
bottom. Old fences may serve as a rough guide to the sur- 
veyor in looking for a corner. 

The evidence of living persons may be accepted in accord- 
ance with their sense of locality, their habits of observation, 
and their ability to determine locality by relative position to 
other objects, but in general, very little confidence can be 
placed in such testimony, and the corner must be considered 
and treated as lost. 

If line trees are found, they are a guide in retracing a line, 
but do not materially aid in determining the locus of a cor- 
ner. Field notes may be sufficiently explicit to guide a sur- 
veyor to the locality. As instance, it describes a stake set in 
the center of a small marsh. Set stake in a hollow, water two 
feet deep, etc. Again, measurements may be checked by 
geographical features described in field notes. Instance, at 
10 chains enter marsh, at 20 chains leave marsh, etc. 

All physical features described in field notes, though not 
absolute, are a rough guide to the surveyor in the perform- 
ance of his work. 

Notwithstanding all our discussions upon the restoration 
of lost and missing corners, a permanent re-establishment 
depends upon acquiescence of interested parties, If the con- 
sent of one be withheld, perhaps another surveyor is called 
upon to perform the work, and the case finally ends with the 
decision of the court. 

In older settled countries it has been a long time custom 
for interested parties to submit their differences to an expert 
surveyor rather than go to law, It would be better for all who 
are interested in boundary disputes to abide by such a deci- 
sion. In many instances where a dispute is not an issue of 



THE SURVEYOR'S GUIDE 59 

fact for the court to decide the defense prefer a jury trial, 
whose decision may not be in accord with facts, but 
honestly more in accord with other influences surrounding the 
case. 

A quarter post was 7 rods and 10 links south of where it 
should have been located. The witness trees corresponded with 
government notes, and it was recognized by several surveyors 
as the corner established by government surveyors. The 
party favored by its location was absent a term of years, and 
upon his return found the stake moved and established where 
it should have been. The original witness trees and corner 
evidently had been purposely obliterated. He employed a 
surveyor familiar with the corner, who by digging, found the 
bottom of the original stake and traces of the original witness 
trees. Other surveyors corroborated the corner, and the 
adverse party was obliged to acquiesce to its original location. 

The question is natural: How could such a gross error 
occur ? In running east the surveyor may have encountered 
local attraction, or he may have run on an erroneous variation. 
He intersected the east line of the section nearly 14 rods 
south of the section corner, but neglected to correct the line 
back and the post remained as established on his random line. 
Corroborative, the post is not equidistant between section lines. 

Generally we find north or south % posts nearer to a 
right line than east or west % posts. The surveyor having 
run east to a closing section corner, naturally returns over 
the line run, and on his way back corrects the ^ post by 
measuring the offset required to bring the post into line. If 
he corrects the % post south, it makes him one mile extra 
travel; as time with him is money, the south ^ post is left in 
its original locus, a cause of many east or west ^ posts 
being so far to one side of a right line. Often the surveyor 
takes sight on a distant tall tree, and pointing it out to his 
chainmen directs them to follow. Coming up to his line 
sight the bottom of his object is 15 or 20 feet to one side of 
the top. Nevertheless, it is marked a line tree, and shows 
the crude method of running lines. 



60 



THE SURVEYOR'S GUIDE 



CORNERS FOR PRAIRIE TRACTS. 

In a prairie, timberless tract corners are designated as 
follows: 



pit 



Pit 








A 



^ 



^ 



Pit 



Corner on a Standard L,in^ 



Pit 



Pit 




V 



A* 



\M 



PiT 



Pit 



Corner common to iour Oections 



Pit 




V* 



. t v i^ oun< 



Pit 



Quarter oectior) Gorner. 



Pit 




I 



\K^ 



Pit. 



«*.- 



Township standard line, stone mound, wood posts in 
center of mound and pits. 



THE SURVEYOR'S GUIDE 



61 



Pir. 




t* r 



*\\** 



>o#' 



Pit. 



Section corner, mound of earth, wood posts in center of 
mound and pits. 



Pit. 




V* 



*\*' 



Pit 



Quarter post, mound of earth, wood post in center of 
mound and pits. 



cpt 



F 



A" 




Stone Post. 

Township corner, mound of stone and stone post. 

P.'r „ J^>° p . 




Section corner, mound of earth, pits and stone post. 



Pit 



k vn Pt 




Quarter section corner mound of earth, pits and stone 
posts. 



62 THE SURVEYOR'S GUIDE 

DEFINITIONS OF SURVEYORS' MARKS. 

S. C. is a standard township corner, 

C. C. is a closing township corner. 

M. C. is a meander corner. 

W. C. is a witness corner, 

S, C. ^ C. B. T. is a standard % section corner, 

S. is a section corner, 

% S. is a % section corner, 

B. T, is a bearing tree. 

R, W. is range west. 

R. E. is range east. 

Six notches on all sides of a corner stake is a corner com- 
mon to four townships. The number of notches on the south 
and east sides of a corner indicate the number of section lines 
north and west of the south and east line of the township. 

Line trees are marked with two chops or notches or blazes 
cut on each side about four feet above the ground. 



CHAPTER IX. 

SURVEYING AND SUBDIVIDING LANDS BY METES 
AND BOUNDS. 

Note. — The term metes and _ bounds "is length, or 
dimension, or limits, boundaries." 

All enactments of Congress concerning the survey of 
"public lands," though differing somewhat in plan of subdi- 
viding, recognize one principle, "due north and south and 
east and west lines," 

Lands not included in said enactments have generally been 
surveyed by metes and bounds, describing irregular boundary 
lines of land grants and their future subdivisions. These 
grants have been subdivided, and sub-subdivided into small 
tracts to suit the locality and desire of the purchaser, until a 
majority of them contain as many, if not more angles than 
acres; hence it is plain the boundary lines of this system 
must be very irregular and run on many points of compass. 

The original survey of many of these tracts was made 
more than two centuries ago. Suppose one of these divisional 
lines is now lost and a disputed line between parties it bounds: 
How can the original be retraced ? 

The variation of the needle is not always constant, but at 
intervals of perhaps a century, it reaches a maximum or 
minimum and then changes, so that at some future time, 
when now it is increasing or decreasing, it will be reversed, 
/, e., when increasing it will annually decrease and vice versa, 
annually increase, 

RULE FOR RETRACING A SURVEY DESCRIBED BY 
METES AND BOUNDS. 

First take the bearing of one or more undisputed lines of 
the tract to be resurveyed and the difference between it and 
the original will be the degrees and minutes to set your 
vernier. 

Note. — If the variation is increasing, the variation will be 
greater; if decreasing, it will be less; if increasing, the varia- 
tion is west; if decreasing, it is east, 

63 



64 THE SURVEYOR'S GUIDE 

Commence at the initial corner of the survey and run the 
original bearings. 

Note, — If it is a disputed corner take the one next near- 
est. Compute the latitude and departure. The northings 
and southings ought balance, and the eastings and west- 
ings ought balance also. If they do not, you must make the 
proper corrections and balance them; pursue the same 
method with the other tract and the disputed line ought 
agree. If it does not, there is an error in the original survey. 

Where practical, measure the included angles of the 
undisputed lines in place, and compare them with your 
surveys. This will detect errors in latitude or departure. 
Correct accordingly, until the true course of the disputed line 
is obtained agreeable with the two surveys, 

In most instances, when the courses have been correctly 
surveyed and recorded true bearings, it is less complicated to 
retrace an old survey than re-establish a lost corner of a 
section, 

Observe, only one principle controls a resurvey of an old 
tract of land described by metes and bounds, viz., "variation of 
the needle" at the time survey was made. Wherever the 
bearings of one or more of the courses can be obtained, the 
difference between it and the original will be the degrees and 
minutes to set you vernier. Generally the boundary lines of 
these old tracts, by long-continued occupancy of the land they 
bound, are as firmly established as the rock of Gibraltar, and 
no power on earth (except earthquakes or deeds of con- 
veyance) can change them. 

PERMANENT STARTING POINT NECESSARY FOR 
METES AND BOUNDS. 

A survey by metes and bounds should have a well defined 
and permanent starting point; and from thence the courses 
and distances accurately described. The bearings should be 
recorded true bearings that at any time the lines can be cor- 
rectly retraced. 

Note. — // is obvious that the variation must be known. 



THE SURVEYOR'S GUIDE 



65 



The description of tracts surveyed by metes and bounds 
are often amusingly defective, and the initial point meaning- 
less. 

Instance, a deed describes a line starting at a birch tree 
near a brook. 

A certain rock on the bank of the river with the top 
knocked off. As the supposed rock is a ledge similar in 
character, the point is clearly lost as a lost section corner. 

LATITUDE AND DEPARTURE. 

Latitude and departure is the distance a course has made 
due north or south and east or west between its initial 
points and terminus. The distance of a course is the radius 
of a circle, and the bearing the angle it makes with the true 
meridian, in which the departure is the sine of the angle and 
the latitude its course. 




Let AB= the distance or course = radius .-. A C = the 
latitude, B C the departure and B A C the angle = the true 
bearing. By formula in the solution of Right Triangles we 
have: 

Departure B C = length of course X sine of bearing. 
Latitude A C = length ol course X co-sine of bearing. 



66 



THE SURVEYOR'S GUIDE 



EXAMPLE. 

Given the bearing N. 20 W, and distance 30 Rods. 
30 R. X sine of 20 = 10.260 departure. 
30 R. X co-sine of 20 = 28.190 latitude. 

By this formula the traverse tables are computed. 

It is plain, that in surveying a tract of land you travel south 
the same distance as you do north, and the same distance 
east as you do west . *. it is evident that east and west depar- 
ture should balance, and north and south latitude balance 
also; if they do not. the error should be distributed propor- 
tionate among the sides, i. e., bearings and distances. 

EXAMPLE. 

Given the bearings and distances of a tract of land as per 
diagram to correct latitude and departure 

FIG. I. 




£ A-0 cNs 



W 

2 0,40 c^ 




THE SURVEYOR'S GUIDE 67 

Corrected latitude and departure as per following table: 





Beanrjeb 


i 


. — . ._. — 


Departure 


N 


S 


£ 


w 


/ 


M /o°£ 


>?0*o 


/9J? 




350 




* 


£ 


V0 






*fO t OO 




3 


S/S°£ 


30,30 




*?.*6 


7.91 




1 


53o°W 


ZO 




'7,3* 




70,00 


5 


tilo'W 


10 


9.39 






3,1 X 


6 


W 


zo.vo 








10,HO 


7 


N </5°Jl* H< 


X9,60 


77,* 8 
.on 






OK 



V*"*' U.SB SI. 3^ Sl.3%- 

As there is only an error of .02 in northings and south- 
ings and .02 in eastings and westings, add it to the eastings 
and westings of last course and balance latitude and depar- 
ture. 

Suppose the bearings remain the same, except course 2 is 
S. 88° E. The latitude will be 1.39 and departure 39.97. 
The northings are now 46,58, and the southings 47,97, the 
eastings 51.3c, and westings 51.32. 

The difference in latitude is 1.39, and departure 0.01 only. 
It is evident the error is in the most easterly bearing g^- 3 7 9 T = 
nat. tang. = 2 nearly. The error is in second course, and 
should have read E. 

SURVEYS BY TRIANGULATION. 

The survey of the State of Massachusetts by triangulation 
was one of the most scientific in the United States, as the 



68 THE SURVEYOR'S GUIDE 

entire system depended upon an exact measurement of a base 
line, it was measured with glass rods, and mathematical 
precision obtained. Observatory stations were established 
upon several of the highest points, and angles measured with 
great care; but as the calculations and work are without the 
comprehension of an ordinary land surveyor, further explana- 
tions are useless. Suffice, the shore lines of our great fresh 
water lakes and rivers are surveyed by this system; the most 
perfect that can be devised. 



CHAPTER X. 

CONTENT OF LAND. 

10 square chains is one acre. 

160 square rods is one acre. 

43,560 square feet is one acre. 

The side of a square acre is 3 chains, 16 links. 

The side of a square acre is 12 65-100 rods. 

The side of a square acre is 208 7-10 feet. 

TO LAY OUT A SQUARE ACRE. 

Measure the sides 3 chains, 16 links ; or 12 65-100 rods ; or 
208 7-10 feet, forming four right angles. 

Given one side of a parallelogram or rectangular tract of 
land to enclose a. given area: 

RULE. 

First reduce the given area into square chains, square rods, 
or square feet and divide by the given side. 

EXAMPLE. 

The given number of acres is 10 and the given side is 4 
chains, or 16 rods or 264 feet. 

10x10 = 100 -1- 4 = 25 chains, the required side. 

160x10 = 1600 _^ 16 = 100 rods, the required side. 

43560x10 = 435600 -^- 264 = 1650 feet, the requried side. 

To find the contents of a tract of land with two parallel sides 
of unequal length forming a trapezoid, 

RULE. 

Add the two parallel sides together and multiply half their 
sum by the perpendicular distance between, 

EXAMPLE. 

One of the parallel sides is 10 rods the other 30 rods and 
the perpendicular distance 40 rods. 

-- — — = 20 X 40 = 8co -f- 160 = 5 acres. 
2 J 

GO 



70 



THE SURVEYOR'S GUIDE 




To find contents of a tract in shape of a trapezium, in 
•which no two sides are parallel. Measure diagonal A C, then 

multiply diagonal by the sum of 
the two perpendiculars A B and 
D C, and divide by 2. 

Given the two legs of a right tri- 
angle to find contents. Rule: 
Multiply one-half the length of one 
leg by the other. 

EXAMPLE. 

Given the length of one leg 40 rods, the length of the 

other 30 rods, — X 30 = 600 -f- 160 = 3 ^1 a. 
J ' 2 ° 100 

To find the contents of a tract of land, one side of which 

is bounded by a stream very irregular in its course: 

RULE, 

Run a random line parallel to the general course of the 
stream, and at intervals along said line at right angles, meas- 
ure the distance from off it to the river; you now have several 
consecutive figures and the main body — having two parallel 
sides and base to find contents, their sum will be required 

contents, 

EXAMPLE. 

Suppose you have a fractional forty, one side of which is 
bounded by a meandered stream as per 

FIG. I. 




THE SURVEYOR'S GUIDE 71 

Fig. i B a c - X i = j.oo square chains. 
2 Bde a ^±- x X 2 = 3.00 " 
3 clf ge^x 3.5= 5.25 " 
4fhk g?±-° X 4 =4.00 ", 

5 him k 3±° X 4= 6.00 " 

J 2 

6 lno m 2+1 X 4 =8.00 " 

2 

7 mpos^ X 3= 5.25 " 

8 C p s 2 -5 X 1 = 1.25 " 

A B C D = 7 -+I- 5 X 20 = 220.00 " 
2 

253-75 = 25 H a. 
100 

TO FIND THE AREA OF A CIRCLE 

Multiply the square of the diameter by the decimal ,7854, 

EXAMPLE. 

The diameter of a circle is 40 chains. What is the area? 
40 X 40 X .7854= 1256,64 square chains = 125 — a. 
To lay out a given area in the form of a square: 
Rule : Reduce the given area to square chains, rods or 
feet, and extract the square root. You then obtain the length 
of the sides, 

EXAMPLE. 

Given area is 10 acres, 10x10= 100 square chains, the 
square root is 10, the length of a side ; or 10 acres = 1600 
square rods, the square root is 40, the length of a side ; or 10 
acres = 435600 square feet, the square root is 660 feet, the 
length af a side. 

To lay out a given area, the adjacent sides to have a given 
ratio: 

Divide the given area expressed in square chains, rods or 
feet by the product of the numbers expressing the ratio, The 
square root of the quotient multiplied by these numbers, 
respectively, will give the length of the sides. 



72 THE SURVEYOR'S GUIDE 

Given the area 10 acres and the sides as 3 to 2. 

10 X 10 = 100 -1-6= / 16.666 = 4.082. 

10 X 160 = 1600 t6= / 266.666 = 16.33 r °ds. 

10 X 43>5 6 ° = 435> 000 -*- 6 = / 72,606 = 269.44. 
3X2=6 4.082 X 3 = 12.246 chains one side. 

4.082 X 2 = 8.164 " other side, 
or ID -33 X 3 = 49 rods one side. 

16.33 X 2 = 32.66 rods other side, 
or 269.44 X 3 = 808.32 one side. 

269.44 X 2 = 538.88 other side. 

Given a Trapezoid to be divided into two equal parts by 
a line parallel to a given side. 




By formulae: 

2BC2 + 2 AD2 = E p2 

2 + 2 
B C— A D : F E— A D : : A B :" A E 

BC=2o AD = 10 Ratio 2 to 2 

2X20X20=800 2X10X10 = 200 + 800-^4=250 

/ 250 = 15.49 = E F. 20 — 10 = 10 : 15.49 — 10 = 5.49 : 
20 : 10.98= A E 

20 — 10 = 10 : 1549 — 10 = 549 :: 19 : 10.43 =DF 

To compute a tract of land by latitude and departure. 

Given a tract of land, the notes of which and corrected 
latitude and departure are found on page 67, 

Rule : If the departure of the first and last courses are E, 
or W, , add them together and place their sum in the columns of 
double departures of the same E. or W., but if one be E., the 



THE SURVEYOR'S GUIDE 73 

other W., subtract them, and place the difference in the col- 
umns of double departure of the name of the greater ; pro- 
ceed in the same manner with the other courses, and if the E, 
or W. columns of double departure balance, the work is 
correct. 

Assume any number (say o) for the first course, marking it 
E. for East, then if this multiplier and double departure are 
both E,, add them together and place the sum in the columns of 
multipliers, marking it E.; but if the multiplier and double 
departure are one E., the other W., subtract and place the 
difference in the column of multipliers, marking the name of 
the greater, i. <?,, if W. be greater, mark it W, Proceeding 
the same manner until all the multipliers have been found. 
The last multiplier will be equal to the first double departure, 
but of a different name, i. e., E. or W. Multiply the 
latitude by the multiplier, and if multiplier be E. place it in 
the column of latitude of the same name as the latitude, 
if W. and latitude is N. place it in the column of S, latitude. 
If S, place it in the column of N. latitude; half the difference 
of their sums will be the area of the tract. 



74 



THE SURVEYOR'S GUIDE 



CONTENT OF FIG. 7. 



^6 






no 


<5> 








o 










<*> 






\0 


«0 


in 






UJ 
K 


«4 


UJ 


Q 








\0 








Q 
Q 
Ul 




o 

JO 












£ 










JO 


o 




UJ 


5 


3t» 












<0 






NO 


fa 








^ 


■v. 








fa 




JO 




o 

N 
O 








^ 

\ 






o 
£0 





<u 


<0 


o 

<0 


o 


^ 






■^» 


«>< 


fo 


^ 


io 


\0 


J- ! 
i 



i4' 

5»- 



fc- 


* 


f4 


vS 


pv 


^ 


sa 


I^V 


c* 


N* 


n 


\ 



^ 



Ft 


<C 


o--. 


«)s 




ro 




Vi 



«0 



THE SURVEYOR'S GUIDE 75 

Metes and bounds often more reliable than a township 
survey. A resurvey of a tract of land described by metes 
and bounds is less complicated than the re-establishment of a 
lost corner. 

Generally the work has been done with more care, and if 
true bearings have been given", and the variation noted, 
seldom is there any difference in surveys, hence seldom a 
disputed boundary line. 

In many respects a survey described by metes and bounds 
is more reliable than imperfect work of township sub- 
divisions. 



CHAPTER XI. 

Simple methods to measure the distance across a stream 
or other obstruction. 



Ffg I. A 



F-5-2 




f ISO IkS 



D E. 




FIG. 4. 




Measure off perpendicular 
AC, D E, ranging the point 
C in line with E B 

then AB= A C X A D 
I) E — AC 

In right angled triangles 

Hypoth 2 =base 2 +perpendic 2 . 

Base 2 =•= (hyp + perp) X (hyp 

— per) perp 2 = (hyp + ba) X 

(hy-ba). 

Fig. I. Measure A B and at B at right angles to A D, 
Measure C B; measure D E. Rule as C B : A B :: E D, 
A D — A B=DB, the distance across river. 

Fig. 2. At A and at right angles to A D, measure A B. 
At C, in line with A D, set a stake, measure E D = A B, so 
the point D will be in line with C A, and the point E in line 
with C B, then measure C D = A C, the distanee across the 
river. 

Fig. 3. xAt A in line with C D throw off a right angle 
A B, set up at B and make the angle A B C = angle A B D. 
Measure A C = the distance AD across the river, or measure 
the length A B, and at B measure the angle A B D, and at D 

76 



THE SURVEYOR'S GUIDE 



77 



measure the angle A D B. You have the side A B of a right 
angle triangle, and angle A D B to find A D. Multiply the 
side A B by the co-tangent of the angle A D B = A D, the 
distance across the river. Suppose A B is 500 feet and the 
angle A D B = 20 , natural co-tangent of 20 , is 2.74748 X 
500 = 1373.74 feet, the distance across the river. 

Several other methods can be adopted, but in general appli- 
cation the above are sufficient. 

OBSTACLES IN LINE. 
FIG. 5. 
C 




At a, measure the angle cab= 6o°, measure a c = one 
chain, at c measure the angle acb= 6o°, measure c b = one 
chain, at b measure a b c = 6o°, then a b is one chain and in 
the same straight line as A B. The figure is an equilateral tri- 
angle. Or at A set off a right angle 10 or more links so as to 
clear the point d. At B set off a right angle 10 or more 
links, making the line C D parallel to A B. 

To measure 
angles with a chain. 
Prob. I. To lay off 
a right angle to a 
given line A B. 
On the line A B 
3 measure the dis- 
tance a b=6o links, 
b d = 80 links, ad= 100 links, then d b is at right angles 
to A B; or make a b and b c equal — then with a longer radius 
as a d and c d describe arcs cutting each other at d, then d b 
will be perpendicular to A B. 




78 



THE SURVEYOR'S GUIDE 



Prob. 2. 



To describe angles of 30 , 6o° and 45 . From 
A with any radius A o, describe 
o a, and from o with a like 
radius, cut it at a, let fall per- 
pendicular a S, then a A S = 
6o°, A a S = 30° Make A S 
and a S equal — then a A S and 
A a S = 45 . 




LEVELING. 

The art of leveling really belongs to the engineer, who is 
supposed to possess the necessary instruments. But to ascer- 
tain the difference of level between two given points the sur- 
veyor can substitute a carpenter's spirit level and obtain close 
approximate results. At each end screw into the level large 
head screws until the top of head is about one-half inch above 
the face edge of level thus | ^ | Set level top of 
compass, and bring bubble into center of tube. Take a sight 
on rod, fix target, then reverse the level, if sight now bisects 
the same point on rod, the top of screws (your line of sight) is 
parallel with the level; if it does not, lower one of the screws 
until reversal bisects the same elevation. 

Mark a ten-foot pole into feet, tenths and hundredths 
(decimals are more convenient than inches). For target use 
thick white paper, which the rodsman slides up or down until 
it coincides with line of sight ; observe the reading, i, e., the 
feet, tenths and hundredths it is above the peg upon which 
the rod is held and note it in the proper column of back or 
fore sights. 

As near as practicable the distance to fore sights should equal 
the distance to back sights. Back sights are those looking 
toward your starting point. Fore sights are those looking in 
the opposite direction, The difference between the sum of 
back sights and the sum of fore sghts is the rise or fall between 
the two 'points of survey. 



THE SURVEYOR'S GUIDE 



79 



The curvation of the earth's surface, independent of refrac- 
tion, is computed at 8.004 inches for I geographical mile; 
an apparent level is tangent to the earth's surface, and a true 
level is parallel with the surface; by taking a distance of 
equal back and fore sights, practically you obtain a true level. 

ILLUSTRATION. 




J3ac/{ Sights 


/5re 


Sights 


Disr. 


— t 
Rise or Fall 


A A H,^ 

Bb 5.H 
Cc 3,6 


a 6 
b C 
c D 


3. 1 
8,6 
5.5 


A00 
150 
500 


A B + /, / 
BC - 3,x 
CD - /.<? 


'3,* 




I7.X 

/3.A 


750 


- v 


H 0, 



+ is higher; — lower ground. 

With a carpenter's spirit level very close results can be 
obtained. 

The following formula may be of utility to the surveyor 
in constructing highway bridges: 



2000 b d 2 
X 



Safe load. 



3 " b 

b = breadth, d = depth and c = length of a beam. The re- 
sult is the safe load in lbs. at the middle. 



80 



THE SURVEYOR'S GUIDE 



TIME OF EXTREME ELONGATIONS OF THE NORTH 
STAR— YEAR 1894, LATITUDE 44°. 



A\onTq. 


JO&y cf Wee./^ 


FtrsT. 


£/eve.ntk 


Twenty -Tirsf. 


£L 


W. 


£.. 


8 w. 


EL. 


W. 


Jd,l\ 


0.57™ 


0,29 AM 


//.57 AM 


t/.HS-PM 


//./SAM- 


1 106 PM 


FeL 


/0,3V AM 


/0,2.3 PM 


?,S5" 


W3 » 


9/6 „ 


9,ov ,. 


M&rr 


Ml - 


d,5z .- 


2,05- 


7,53- 


7*5 .1 


71H - 


fyrt/ 


6.4/ * 


6,50 » 


6,03- 


5,51 '/ 


5.ZH : 


5,/2, - 


M&y. 


4,W >• 


4, 32 " 


4,05 ■• 


3,33" 


3,25- 


3/Y " 


<Jur\e. 


Z^3 " 


*, 31 ■■ 


203 ■■ 


J,s-x - 


/,Z4» 


A/2. •• 


Jv/y. 


<5,VV - 


33- 


/ZpifW, 


//,33AM 


/1.23 PM 


//,/iAM 


#u$ 


f&,46PM 


/O, 32 AV 


/0,OI „ 


<?,S3 » 


9*1 " 


?J3 " 


Sept. 


8.38 , 


85o ,, 


y.s<j: 


7,*t ■' 


7./f " 


X'f •> 


Oct. 


6,40 , 


6,32 '• 


6,0/ ,. 


$.53.. 


52X •• 


S,/Y« 


Nov. 


4,3 S >■ 


4.31 >• 


359 •• 


351 ■■ 


3J0 ,. 


3. II » 


It« 


Z.fo ,. 


2,32 - 


z\ot <• 


7,53 •■ 


/,ZX <• 


/./*/ << 



For the year 19.00 add 7/ change of latitude, affects the 
time only slightly. The above time will be found sufficiently 
close for practical application. . 



THE SURVEYOR'S GUIDE 



81 



AZIMUTH OF THE NORTH STAR FOR ANY YEAR BE- 
TWEEN 1890 AND 1905 AND FOR ANY LATI- 
TUDE BETWEEN 25° AND 50*. 



Lat 


/89+ 


1895 


I8S6 


1897 


1698 


1899 


1900 


1901 


I90X 


/903 


lyet 


11 OS 


x°s 


/Vj' 


7°Z3 


/•zj 


/'ZZ 


/°ZZ 


/'Zl' 


/°ZI 


/'Z/ 


/'ZO' 


/°Z0 


/'zo' 


/•/I 


26 


/'Z.V 


/'z« 


/°Z3 


/•As' 


/'ii 


7'Zz 


7'ZZ 


/'Zl 


7'Z/ 


/'Z/ 


/'zo 


/'iO 1 


*r 


/'is 


/°IH 


/°Zi 


l'Z.3 


7°13 


/°A5' 


/°zz 


/°ZX 


/'zz 


/"Z/ 


/'Zl' 


/°Zl' 


Z8 


/'ZS 


/'ZS 


/'is 


/'Zl' 


/VY 


/°Z1 


7°Z3 


/°Z3 


/'Z37 


/°zz 


7'ZZ 


rzx 


29 


/°Z6 


l°Z(,' 


/°Z5 


/°ZS 


/°ZS 


/*W 


7°Z9 


/"zv 


7'Z.t 


7'Z? 


7'A% 


/°j& 


20 


/'A?' 


n/ 


/°Z(, 


/°Z6' 


7°Z(, 


/'zs 


/'ZS 


i'ZS 


/°zr 


/'*¥ 


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3' 


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7°Z7' 


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7'z; 


7°Zb 


7°Zb 


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7'ZS 


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33 


7 '30 


7 "3d 


rZf 


7'Zf 


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7'JLS 


*'*? 


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36 


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38 


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7 "33 


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10 


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7'3f 


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7 'J 7 


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7*35 


7'35 


7'Ji' 


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11 


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/ c i0 


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7 '37 


7 "5 7 


7°J7 


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f3sr 


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7'37 


13 


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CIS 


/°1X 


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/"to 


/'to' 


/'J? 


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11 


/°Vf 


/'■¥</ 


/*VV 


/°V3 


t'*3" 


/°13 


7"/X 


/•is! 


/•■v/ 


/'*/' 


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/'it 


Is 


/°v 


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7'V3 


/•i3 


7°i3 


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1 6 


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''V 


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/"/r 


/•if 


7'iJ 


7'Vi' 


/*t¥ 


</7 


7°Jo' 


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nr 


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n? 


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/•>a' 


V? 


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'°J1 


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/'So' 


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m 


/'ft' 


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<"} 


/°jj 


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''S3 


/°S3 


7"JX 


>'SK 


/'J A 


7'S/' 


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/'Sd' 


7 '30' 


So 


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rs 7 


7°3(,' 


/°J6' 


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7'JT' 


/'jr 


7'JY 


/'j-y 


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/'JZ' 


7'JZ 



Decimal of a minute is omitted and the nearest whole 
number given. 

The annual decrease is about o° oo.4 / . 



82 



THE SURVEYOR'S GUIDE 



THE CHAIN AND LINKS REDUCED TO FEET. 

A surveyor's chain is four rods = 66 feet long and con- 
tains loo links each 7 — inches long. 

' 100 & 



b*{: 


/ 


X 


3 


1 


s 


10 


IS 


3.0 


A5 


30 


35 


^YO ] 


Fee-t 


0(b 


i.3Z 


/■t? 


*6V 


J 3 


6 6 


1.9 


S3.* 


/6S 


/13 


Z3I 


Zb.t\ 


M* 


45 


JC S3 i €0 


65 


70 


7S 


80 


8s 


to 


15 


,00 \ 


l/Sef 


X9.7\ 33. .-5*3 !3?,6 


**9 


tti. 


V9S 


Si 8 


S6/ 


^ff 


6*7 


66 8 



Suppose your measurement is 99 links 

The nearest number is 95 " =62.70 

Tabular number for 4 " = 2.64 

99 links = 65.34 feet. 

Suppose measurement is 83 " 

The nearest tabular number is 80 " =52.80 

Tabular number for 3 " = 1,98 

83 = 54.78 

Links are decimals of a chain. Multiply chains and links 
by 66 feet and point off two decimals, 3 chains 35 links X 66 
= 221. 10 feet, or 3 chains = 198 + 23.1 = 221.10. 



THE SURVEYOR'S GUIDE 



83 



DEPARTURE FOR 1' TO 30' AT 10 TO 80 CHAINS. 





CK 


CK 


CK 


CK 


CK 


CK 


CK 


c\ 


Mmutis 


10 


10 


30 


40 


5.0 


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60 


1 




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5 




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6 


7 


4- 


1 - 


ih 


34c 


1% 


6 


7 


8 


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5~ 


\K 


3 


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5% 


7Vi 


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10 


" X A 


6 


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34 


syi 


7 


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76% 


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7 


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4- 


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16*3 


& 


ih 


4% 


7 


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tt 


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78% 


9 


1% 


5* 


?% 


'oyx 


75 


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XI 


10 


3o 


58 


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xoy 3 


Z3% 


ii 


sf* 


4/3 


?% 


«# 


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7W 


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7 


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77% 


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3'// 


7£ 


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IA- 


4- 


8 


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S# 


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3oy x 


35- 


)( 


4% 


9/3 


l*t 


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*3fy 


X8~ 


3*y* 


37% 


17 


5 


yo 


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71% 


™% 


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»% 


18 


Sff 


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ts% 


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xe% 


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3<>% 


HX 


19 


5h 


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XX 


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33 


26% 


f+% 


ao 


5 3 / 


i/y 3 


Ml 


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3J 


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K% 


21 


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x<i£ 


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*% 


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13 


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36$ 


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37 


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39 


<isy x 


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6°% 


27 


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3iy 3 


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63 


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19 


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25 
1 


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H3% 


s*y 3 


67 


70 



Suppose 
her is o J 24 



at 50 chains you are 35 links to left tabular hum- 
Tables are expressed in links. 



84 



THE SURVEYOR'S GUIDE 



DEPARTURE FOR 31' TO 60' 


AT 10 


TO 80 


CHAINS. 




ch 


CA 


c 1 


C* 


cV 


C>f 


<-\ 


c \ ] 


Al»Vte. 


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30 


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60 


70 


80 


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9 


18 


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59 


63 


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xr 


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my x 


56 


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67 


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3?y x 


w/ x 


59 >/ 5 


69 fy 


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30% 


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si 


61 


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36 


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68 


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**% 


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3-3y x 


67 


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97 


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99% 


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'ty x 


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13% 


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7/6% 


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89 


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15 


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90% 


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S3 


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vtfy 


«% 


77 


9xy x 


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97 


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1** 


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110 


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5$ 


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3X 


H8 


69 


do 


96 


ux 


IX? 


S c 


I6fy 


32'Sj. 


V? 


63 


8iy* 


97% 


vy 


/30% 


*7 


/&%. 


5.3 


ft% 


6&y 3 


83 


99y x 


116 


133 


58 


17 


33% 


3-0% 


&7y x 


SH*J 


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68% 


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703 


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6o 


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3S 


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7o 


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/»9% 


/XxiL 


/90 

' ... 



Very seldom will departure exceed 140 links. Suppose a 1 
40 chains you are 40 links at the right tabular numbers is 
o° 34 r - 



THE SURVEYOR'S GUIDE 
DIAGRAM. 
A territory subdivided into townships. 



85 



43 JZ 



H°30 



£/»! 


(, fn 


6 M 


6/M 


6 *» 


f, m 


(,M 


6 "1 


5 






T 10 


N ' 








5 

•o 






Tf 


- N 
10 














T? 


o 

N 
a) 














T7 


"a 

o 
■J 








VS 






T 6 



^4 
















c- 














T 5 


5* 
















« 








5 






T H 


% 








5 






T 3 


N 








5 






T I 


N 








5 


3w 


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1 YY 


N 

i a. 


Z C 


3 £ 


f.C 



H3XZ 






v Latitude. fX' 30' 



CK 



ae 



& 



It was intended to insert a full set of " Traverse Tables," 
but it has been deemed advisable to omit them. They are 
not necessary in the field, and practically only in the office. 
In a pocket edition they add bulk and expense, and no special 
advantage; it is better to consult other tables outside than 
add bulk to a pocket edition ; besides the simple rule herein 
given for finding the angle of departure, obviate the necessity 
of "Traverse Tables" for most of the problems required in 
running lines. 



86 THE SURVEYOR'S GUIDE 

LEGAL EVIDENCE AND OPINIONS. 

Witness trees to a corner. 

Line trees to a boundary line. 

Meander posts to a boundary line. 

The law cannot satisfactorily determine in all cases 
whether course or distance shall control when they do not 
correspond. This must be determined by concurring testi- 
mony and the circumstances of each particular case. The one 
that convinces the judgment most, must be selected, McCin- 
tock vs. Rogers, nth 111. Reports, Peck. 

Each section or a subdivision of a section is independent 
of any other section in the township, and must be governed 
by its marked and established boundaries. Should they be 
obliterated a last recourse must be had to the best evidence 
that can be obtained showing their former situation and 
place. Lenen vs. Smith, 7 Port. (Ala.), 428. You are not 
to locate a corner but decide where it was. 

The rule that convinces the judgment most clearly is the 
one to apply. 

Surveyor-General to C. C, Palmer: You will place the 
corner where the weight of evidence places it. 

Every lost corner may require a different application of 
principle to determine its original locus. 

Supreme Court decisions of states do not, in all cases, 
agree. 



Eugene Dietzgen Co., 




16 Dearborn Street, 
CHICAGO, ILL. 



Manufacturers and 
Importers of 



Drawing Materials and 
Surveying Instruments. 

Complete Illustrated Catalogue and Price List, and Sample Book of Drawing 

Papers mailed to Dealers and Professionals of good 

standing on application. 




Pocket Book Style— Open. 

Highest Class of Levels and Transits, 

Tapes, Chains, Rods, Plumb Bobs, 
Aneroids, Surveying Compasses, 
Drawing and Tracing Papers and Cloths, 
Blue and Black Print Papers, 
Mathematical Instruments, Scales, 
Rules, Protractors, Triangles, Curves, 

T Squares, Straight Edges, Pencils, 
Drawing Boards and Tables and Inks, Etc. 






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